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Index of articles associated with the same name
Open mapping theorem may refer to: Open mapping theorem (functional analysis) (also known as the Banach–Schauder theorem), states that a surjective continuous
Open_mapping_theorem
Condition for a linear operator to be open
In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz
Open mapping theorem (functional analysis)
Open_mapping_theorem_(functional_analysis)
Theorem on holomorphic functions
In complex analysis, the open mapping theorem states that if U {\displaystyle U} is a domain of the complex plane C {\displaystyle \mathbb {C} } and f
Open mapping theorem (complex analysis)
Open_mapping_theorem_(complex_analysis)
Mathematical theorem
complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number plane
Riemann_mapping_theorem
Area of mathematics
Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered
Functional_analysis
Mathematical function that preserves angles
of conformal: a mapping f {\displaystyle f} which is one-to-one and holomorphic on an open set in the plane. The open mapping theorem forces the inverse
Conformal_map
Theorem relating continuity to graphs
spaces, then the theorem can also be deduced from the open mapping theorem for such spaces; see § Relation to the open mapping theorem. Non-Hausdorff spaces
Closed_graph_theorem
Mathematical theorem in complex analysis
as a special case of the open mapping theorem, which states that a nonconstant holomorphic function maps open sets to open sets: If | f | {\displaystyle
Maximum_modulus_principle
Theorem about metric spaces
Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important
Banach_fixed-point_theorem
Theorem about zeros of holomorphic functions
Rouché's theorem is to prove the open mapping theorem for analytic functions. We refer to the article for the proof. A stronger version of Rouché's theorem was
Rouché's_theorem
Theorem stating that pointwise boundedness implies uniform boundedness
Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered
Uniform_boundedness_principle
Theorems connecting continuity to closure of graphs
graph theorem employs the open mapping theorem. It simply uses a general recipe of obtaining the closed graph theorem from the open mapping theorem; see
Closed graph theorem (functional analysis)
Closed_graph_theorem_(functional_analysis)
Functions that send open (resp. closed) subsets to open (resp. closed) subsets
functional analysis, the open mapping theorem states that every continuous linear surjection between Banach spaces is an open map. This theorem has been generalized
Open_and_closed_maps
Type of function in mathematics
domain, then they agree everywhere on that connected open set. This is a form of the identity theorem. However, analytic continuation need not be possible
Analytic_function
Generalization of closed graph, open mapping, and uniform boundedness theorem
and convex analysis, the Ursescu theorem is a theorem that generalizes the closed graph theorem, the open mapping theorem, and the uniform boundedness principle
Ursescu_theorem
Theorem in complex analysis
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard
Cauchy's_integral_theorem
Theorem about the range of an analytic function
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after
Picard_theorem
Power series with negative powers
contour γ {\displaystyle \gamma } is an immediate consequence of Green's theorem. One may also obtain the Laurent series for a complex function f ( z )
Laurent_series
Functions in mathematics
principle; a theorem of removal of singularities as well as a Liouville theorem holds for them in analogy to the corresponding theorems in complex functions
Harmonic_function
Concept in complex analysis
Riemann–Roch theorem. Argument principle Control theory § Stability Filter design Filter (signal processing) Gauss–Lucas theorem Hurwitz's theorem (complex
Zeros_and_poles
Concept of complex analysis
proof. The statement is as follows: Residue theorem: Let U {\displaystyle U} be a simply connected open subset of the complex plane containing a finite
Residue_theorem
Theorem limiting types of conformal mappings in Euclidean space of dimension > 2
In mathematics, Liouville's theorem, proved by Joseph Liouville in 1850, is a rigidity theorem about conformal mappings in Euclidean space. It states
Liouville's theorem (conformal mappings)
Liouville's_theorem_(conformal_mappings)
Theorem in complex analysis
In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Number of times a curve wraps around a point in the plane
the winding number in the complex plane are given by the following theorem: Theorem. Let γ : [ α , β ] → C {\displaystyle \gamma :[\alpha ,\beta ]\to \mathbb
Winding_number
Statement in complex analysis
Schwarz–Pick theorem (after Georg Pick), characterizes the analytic automorphisms of the unit disc, i.e. bijective holomorphic mappings of the unit disc
Schwarz_lemma
Characterization of surjectivity
importance of this theorem is related to the open mapping theorem, which states that a continuous linear surjection between Fréchet spaces is an open map. Often
Surjection_of_Fréchet_spaces
On topological spaces where the intersection of countably many dense open sets is dense
functional analysis, BCT1 can be used to prove the open mapping theorem, the closed graph theorem and the uniform boundedness principle. BCT1 also shows
Baire_category_theorem
Integral criterion for holomorphy
mathematics, Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a function is holomorphic. Morera's theorem states that a continuous
Morera's_theorem
Branch of mathematics studying functions of a complex variable
complex dimension (such as conformality) do not carry over. The Riemann mapping theorem about the conformal relationship of certain domains in the complex
Complex_analysis
Characteristic property of holomorphic functions
Cauchy–Riemann system, and Liouville's theorem implies, under suitable smoothness assumptions, that any such mapping is a Möbius transformation. One might
Cauchy–Riemann_equations
Morera's theorem (complex analysis) Nachbin's theorem(complex analysis) Open mapping theorem (complex analysis) Ostrowski–Hadamard gap theorem (complex
List_of_theorems
Concept in functional analysis
of considerable importance in functional analysis and the famous open mapping theorem gives a sufficient condition for a continuous linear map between
Topological_homomorphism
Theorem in complex analysis
Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem. The theorem, published
Carathéodory's theorem (conformal mapping)
Carathéodory's_theorem_(conformal_mapping)
Space where open mapping and closed graph theorems hold
designed with the goal of allowing the results of the open mapping theorem and the closed graph theorem to hold for a wider class of linear maps whose codomains
Webbed_space
Complex-differentiable (mathematical) function
holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis. Holomorphic functions are also sometimes referred
Holomorphic_function
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
Provides integral formulas for all derivatives of a holomorphic function
Moreover, as for the Cauchy integral theorem, it is sufficient to require that f {\displaystyle f} be holomorphic in the open region enclosed by the path and
Cauchy's_integral_formula
Theorem in complex analysis
analysis, the argument principle (or Cauchy's argument principle) is a theorem relating the difference between the number of zeros and poles of a meromorphic
Argument_principle
Attribute of a mathematical function
allow the determination of general contour integrals via the residue theorem. The residue of a meromorphic function f {\displaystyle f} at an isolated
Residue_(complex_analysis)
Locally convex topological vector space that is also a complete metric space
results in functional analysis, like the open mapping theorem, the closed graph theorem, and the Banach–Steinhaus theorem, still hold. Recall that a seminorm
Fréchet_space
Type of vector space in math
space to another is an open mapping meaning that it sends open sets to open sets. A corollary is the bounded inverse theorem, that a continuous and bijective
Hilbert_space
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the plane to arbitrary
Uniformization_theorem
Concept in topology
is continuous. Secondly, there is a version of the open mapping theorem or the closed graph theorem due to Kuratowski: a continuous surjective homomorphism
Polish_space
Theorem in mathematics
to prove a fixed point theorem using the contraction mapping theorem. The inverse function theorem is not often stated separately for one variable, because
Inverse_function_theorem
Concept in complex analysis
of potential functions for conservative vector fields, in that Green's theorem is only able to guarantee path independence when the function in question
Antiderivative (complex analysis)
Antiderivative_(complex_analysis)
Map that satisfies a condition similar to that of being an open map
closed) subsets to open (resp. closed) subsets Open mapping theorem (functional analysis) – Condition for a linear operator to be open (also known as the
Almost_open_map
Normed vector space that is complete
for example) and guarantees that the Banach–Steinhaus theorem holds. The open mapping theorem implies that when τ 1 {\displaystyle \tau _{1}} and τ 2
Banach_space
theorem Open mapping theorem (functional analysis) Product topology Riemann integral Time hierarchy theorem Deterministic time hierarchy theorem Furstenberg's
List_of_mathematical_proofs
Mathematical theorem about Banach spaces
\operatorname {im} T} is closed, then it is Banach and so by the open mapping theorem, T 0 {\displaystyle T_{0}} is a topological isomorphism. It follows
Closed_range_theorem
Has no other singularities close to it
important tools of complex analysis such as Laurent series and the residue theorem require that all relevant singularities of the function be isolated. Isolated
Isolated_singularity
Second-order partial differential equation
{\displaystyle u} is harmonic in D {\displaystyle D} , then the divergence theorem implies the compatibility condition ∫ ∂ D ∂ u ∂ ν d S = 0. {\displaystyle
Laplace's_equation
Geometric representation of the complex numbers
giving a contour integral that is not necessarily zero, by the residue theorem. Cutting the complex plane ensures not only that Γ(z) is holomorphic in
Complex_plane
category theorem Open mapping theorem (functional analysis) Closed graph theorem Uniform boundedness principle Arzelà–Ascoli theorem Banach–Alaoglu theorem Measure
List of functional analysis topics
List_of_functional_analysis_topics
coherence theorem says the sheaf O C n {\displaystyle {\mathcal {O}}_{\mathbb {C} ^{n}}} of holomorphic functions is coherent. open The open mapping theorem (complex
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
Ker(T)⊥ → Ran(T) is a bijection, and therefore invertible by the open mapping theorem. Extend this inverse by 0 on Ran(T)⊥ = Ker(T*) to an operator S defined
Atkinson's_theorem
Axiom of set theory
metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem. On every infinite-dimensional topological vector space
Axiom_of_choice
Theorem in topology about homeomorphic subsets of Euclidean space
theorem in topology about homeomorphic subsets of Euclidean space R n {\displaystyle \mathbb {R} ^{n}} . It states: If U {\displaystyle U} is an open
Invariance_of_domain
Concept in topology
See also: Grauert's approximation theorem A basic result here is a theorem of Milnor which says that the mapping space Map ( X , Y ) {\displaystyle
Mapping_space
Multivariate functions can be written using univariate functions and summing
approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function f : [
Kolmogorov–Arnold representation theorem
Kolmogorov–Arnold_representation_theorem
Computational tool
over F = R or C. It is a subtle consequence of the open mapping theorem that the linear mappings {Pn} defined by v = ∑ k = 0 ∞ α k b k ⟶ P n
Schauder_basis
Topological vector space with a complete translation-invariant metric
{\displaystyle (X,\tau )} is a complete topological vector space. The open mapping theorem implies that if τ and τ 2 {\displaystyle \tau {\text{ and }}\tau
F-space
Continuous mappings can be approximated by ones that are piecewise simple
the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation)
Simplicial approximation theorem
Simplicial_approximation_theorem
Homeomorphism between plane domains
quasiconformal mappings in two dimensions is the measurable Riemann mapping theorem, proved by Lars Ahlfors and Lipman Bers. The theorem generalizes the
Quasiconformal_mapping
Theorem
at the point and vice versa.) Among the corollaries of this theorem are the identity theorem that two holomorphic functions that agree at every point of
Analyticity of holomorphic functions
Analyticity_of_holomorphic_functions
Czech mathematician (1925–1999)
linear algebra. Notable early work include generalizations of the open mapping theorem. During 1945–1949, Vlastimil Pták studied mathematics and physics
Vlastimil_Pták
conformal mappings, the area theorem gives an inequality satisfied by the power series coefficients of certain conformal mappings. The theorem is called
Area theorem (conformal mapping)
Area_theorem_(conformal_mapping)
Earle–Hamilton fixed point theorem is a result in geometric function theory giving sufficient conditions for a holomorphic mapping of an open domain in a complex
Earle–Hamilton fixed-point theorem
Earle–Hamilton_fixed-point_theorem
Study of space and shapes locally given by a convergent power series
analytic functions. A fundamental result in the theory is the Riemann mapping theorem. The following are some of the most important topics in geometric function
Geometric_function_theory
Two theorems about families of holomorphic functions
The first, and simpler, version of the theorem states that a family of holomorphic functions defined on an open subset of the complex numbers is normal
Montel's_theorem
Limit of roots of sequence of functions
corresponding limit. The theorem is named after Adolf Hurwitz. Let {fk} be a sequence of holomorphic functions on a connected open set G that converge uniformly
Hurwitz's theorem (complex analysis)
Hurwitz's_theorem_(complex_analysis)
Way to divide polygon into smaller parts
subdivision rule is "conformal", as described in the combinatorial Riemann mapping theorem. Applications of subdivision rules. Islamic Girih tiles in Islamic
Finite_subdivision_rule
On tangency patterns of circles
between any two curves. The Riemann mapping theorem, formulated by Bernhard Riemann in 1851, states that, for any two open topological disks in the plane,
Circle_packing_theorem
Concept in mathematics
The Dehn–Nielsen–Baer theorem states that it is in addition surjective. In particular, it implies that: The extended mapping class group Mod ± ( S
Mapping class group of a surface
Mapping_class_group_of_a_surface
Infinite sum that is considered independently from any notion of convergence
for example, that its radius of convergence is 1 by the Cauchy–Hadamard theorem. However, as a formal power series, we may ignore this completely; all
Formal_power_series
Construction in functional analysis, useful to solve differential equations
bijective, then its inverse is bounded; this follows directly from the open mapping theorem of functional analysis. So, λ is in the spectrum of T if and only
Decomposition of spectrum (functional analysis)
Decomposition_of_spectrum_(functional_analysis)
Operator theorem
of the Pick matrix comes in), and then finally appealing to the open mapping theorem. As such φ {\displaystyle \varphi } is the desired interpolating
Commutant_lifting_theorem
Certain dynamical systems will eventually return to (or approximate) their initial state
In mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, almost
Poincaré_recurrence_theorem
assumptions it follows that f(D) = g(D). Uniqueness in the Riemann mapping theorem forces f = g, so the original sequence fn is uniformly convergent on
Carathéodory_kernel_theorem
Connects the homology of the symmetric groups with mapping spaces of spheres
Barratt–Priddy theorem (also referred to as Barratt–Priddy–Quillen theorem) expresses a connection between the homology of the symmetric groups and mapping spaces
Barratt–Priddy_theorem
homeomorphism theorem for space quasiconformal mappings, its development and related open problems". In Vuorinen, Matti (ed.). Quasiconformal Space Mappings: A collection
Zorich's_theorem
Conformal mappings in complex analysis
Möbius transformations on quotients of hypergeometric functions. This mapping has regular singular points at z = 0, 1, and ∞, corresponding to the vertices
Schwarz_triangle_function
Complete manifolds of non-negative sectional curvature largely reduce to the compact case
In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature
Soul_theorem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Theorems generalizing the Brouwer fixed-point theorem
sets, as well as the Earle–Hamilton fixed-point theorem (1968) for holomorphic self-mappings of open domains. Also, Aniki & Rauf (2019) presented some
Fixed-point theorems in infinite-dimensional spaces
Fixed-point_theorems_in_infinite-dimensional_spaces
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Describes the transverse intersection properties of a smooth family of smooth maps
In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result
Transversality_theorem
Statement on solutions to ordinary differential equations
on R {\displaystyle R} if it fulfills the condition of the theorem. Assume that the mapping f {\displaystyle f} satisfies the Carathéodory conditions on
Carathéodory's existence theorem
Carathéodory's_existence_theorem
In mathematics, the analytic Fredholm theorem is a result concerning the existence of bounded inverses for a family of bounded linear operators on a Hilbert
Analytic_Fredholm_theorem
Algebraic geometry theorem
^{n}} . The theorem of Bertini states that the set of hyperplanes not containing X and with smooth intersection with X contains an open dense subset
Theorem_of_Bertini
Theorem in topology
In topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides
Jordan_curve_theorem
Vector space with a notion of nearness
in general for topological vector spaces: the closed graph theorem, the open mapping theorem, and the fact that the dual space of the space separates points
Topological_vector_space
In mathematics, the (linear) Peetre theorem, named after Jaak Peetre, is a result of functional analysis that gives a characterisation of differential
Peetre_theorem
Nigerian mathematician and senator (1937–2018)
ISSN 0794-7976. ——— (11 August 2010). "Boundedly barrelled spaces and the open mapping theorem". Portugaliae Mathematica. 46 (3). Sociedade Portuguesa de Matemática:
Sunday_Iyahen
Continuous, position-preserving mapping from a topological space into a subspace
In topology, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace
Retraction_(topology)
Theorem in complex analysis
In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application
Borel–Carathéodory_theorem
Strong form of uniform continuity
Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map f : U → Rm, where U is an open set in
Lipschitz_continuity
Mathematical concept
Bieberbach conjecture Koebe quarter theorem – Statement in complex analysis Riemann mapping theorem – Mathematical theorem Nevanlinna's criterion – Characterization
Univalent_function
Banach also gave proofs of versions of the open mapping theorem, closed graph theorem, and Hahn–Banach theorem. Grothendieck, Alexander (1955). "Produits
List of publications in mathematics
List_of_publications_in_mathematics
Bijective holomorphic function with a holomorphic inverse
simply connected open set other than the whole complex plane is biholomorphic to the unit disc (this is the Riemann mapping theorem). The situation is
Biholomorphism
Extends the Jordan curve theorem to characterize the inner and outer regions
Jordan-Schoenflies theorem for continuous curves can be proved using Carathéodory's theorem on conformal mapping. It states that the Riemann mapping between the
Schoenflies_problem
OPEN MAPPING-THEOREM
OPEN MAPPING-THEOREM
Surname or Lastname
English
English : patronymic from Mann 1 and 2.Irish : adopted as an English equivalent of Gaelic Ó MainnÃn ‘descendant of MainnÃn’, probably an assimilated form of MainchÃn, a diminutive of manach ‘monk’. This is the name of a chieftain family in Connacht. It is sometimes pronounced Ó MaingÃn and Anglicized as Mangan.Anstice Manning, widow of Richard Manning of Dartmouth, England, came to MA with her children in 1679. Her great-great-grandson Robert, born at Salem, MA, in 1784, was the uncle and protector of author Nathaniel Hawthorne. Another early bearer of the relatively common British name was Jeffrey Manning, one of the earliest settlers in Piscataway township, Middlesex Co., NJ. His great-grandson James Manning (1738–91) was a founder and the first president of Rhode Island College (Brown University).
Male
English
 Anglicized form of Irish Gaelic Eóghan, OWEN means "born of yew." Compare with another form of Owen.
Surname or Lastname
English (Devon)
English (Devon) : variant spelling of Appling.
Male
Welsh
 Modern Welsh form of Old Welsh Owain, OWEN means "born of yew." Compare with another form of Owen.
Male
Welsh
Variant form of Welsh Owen, possibly OUEN means "born of yew."
Female
English
English short form of Latin Penelope, PEN means "weaver of cunning."
Surname or Lastname
English (common in Lancashire and northern Ireland)
English (common in Lancashire and northern Ireland) : from a patronymic or pet form of Topp, or possibly from an unattested Old English personal name Topping.
Boy/Male
Celtic Welsh
Son of Owen.
Boy/Male
English French
Open.
Boy/Male
English French
Open.
Boy/Male
Welsh
Son of Owen.
Male
Swedish
Norwegian and Swedish form of Old Norse Óðinn, ODEN means "poetry, song" and "eager, frenzied, raging."
Boy/Male
English French
Open.
Boy/Male
English French
Open.
Surname or Lastname
English
English : from Old English Tæpping, an unattested patronymic from Tæppa. Compare Tapp.Joseph Tapping (d. 1678) is buried in King’s Chapel Burying Ground, Boston, MA.
Surname or Lastname
English
English : variant of Penn.Dutch : metonymic occupational name for a clerk or penman, from Dutch pen ‘pen’.Cambodian : unexplained.
Female
Thai/Siamese
Thai name PEN-CHAN means "full moon."
Boy/Male
English French
Open.
Surname or Lastname
English and Irish
English and Irish : probably a hypercorrected form of Lappin.
Boy/Male
English French American
Open.
OPEN MAPPING-THEOREM
OPEN MAPPING-THEOREM
Boy/Male
Hindu, Indian, Sanskrit
Bee
Female
Irish
Irish name CONGALIE means "constant."Â
Male
Yiddish
(ק×זמיר) Yiddish form of Polish Kazimierz, KUZMIR means "commands peace."
Surname or Lastname
English
English : variant of Ussery.
Girl/Female
Indian
Curing, Healing people
Girl/Female
Arabic, Muslim
The Daughter of Al-mahdi
Boy/Male
Indian, Punjabi, Sikh
Preserver of Spring
Boy/Male
Hindu
Light, Shine
Boy/Male
Tamil
Luck, Powerful
Female
English
Variant spelling of English Cindy, SINDY means "woman from Kynthos."Â
OPEN MAPPING-THEOREM
OPEN MAPPING-THEOREM
OPEN MAPPING-THEOREM
OPEN MAPPING-THEOREM
OPEN MAPPING-THEOREM
a.
Open.
a.
Produced by an open string; as, an open tone.
a.
Taking place in the open air; outdoor; as, an open-air game or meeting.
v. t.
To enter upon; to begin; as, to open a discussion; to open fire upon an enemy; to open trade, or correspondence; to open a case in court, or a meeting.
a.
Free; disengaged; unappropriated; as, to keep a day open for any purpose; to be open for an engagement.
a.
Not of a quality to prevent communication, as by closing water ways, blocking roads, etc.; hence, not frosty or inclement; mild; -- used of the weather or the climate; as, an open season; an open winter.
a.
Having the mouth open; gaping; hence, greedy; clamorous.
a.
Not drawn together, closed, or contracted; extended; expanded; as, an open hand; open arms; an open flower; an open prospect.
a.
Not settled or adjusted; not decided or determined; not closed or withdrawn from consideration; as, an open account; an open question; to keep an offer or opportunity open.
v. t.
To spread; to expand; as, to open the hand.
v. t.
To make or set open; to render free of access; to unclose; to unbar; to unlock; to remove any fastening or covering from; as, to open a door; to open a box; to open a room; to open a letter.
v. t.
To loosen or make less compact; as, to open matted cotton by separating the fibers.
a.
Not concealed or secret; not hidden or disguised; exposed to view or to knowledge; revealed; apparent; as, open schemes or plans; open shame or guilt.
a.
With eyes widely open; watchful; vigilant.
a.
Free or cleared of obstruction to progress or to view; accessible; as, an open tract; the open sea.
a.
Biting; pinching; painful; destructive; as, a nipping frost; a nipping wind.
a.
Free of access; not shut up; not closed; affording unobstructed ingress or egress; not impeding or preventing passage; not locked up or covered over; -- applied to passageways; as, an open door, window, road, etc.; also, to inclosed structures or objects; as, open houses, boxes, baskets, bottles, etc.; also, to means of communication or approach by water or land; as, an open harbor or roadstead.
v. t. & i.
To open.
n.
A furnace or oven for fritting materials for glass making.
n.
Open or unobstructed space; clear land, without trees or obstructions; open ocean; open water.