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Probability theorem
continuous mapping theorem states that continuous functions preserve limits even if their arguments are sequences of random variables. A continuous function
Continuous_mapping_theorem
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 {\displaystyle
Brouwer_fixed-point_theorem
Topics referred to by the same term
Mapping theorem may refer to Continuous mapping theorem, a statement regarding the stability of convergence under mappings Mapping theorem (point process)
Mapping_theorem
Theorem in differential topology
of the more general Poincaré-Hopf index theorem. A consequence of the hairy ball theorem is that any continuous function that maps an even-dimensional
Hairy_ball_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)
Index of articles associated with the same name
that a surjective continuous linear transformation of a Banach space X onto a Banach space Y is an open mapping Open mapping theorem (complex analysis)
Open_mapping_theorem
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
Strong form of uniform continuity
Lipschitz continuous. In the theory of differential equations, Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees
Lipschitz_continuity
Extension of the Brouwer fixed-point theorem
Leray–Schauder theorem which was proved earlier by Juliusz Schauder and Jean Leray. The statement is as follows: Let f {\displaystyle f} be a continuous and compact
Schauder_fixed-point_theorem
Mathematical theorem
In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number
Riemann_mapping_theorem
Mapping theorem in topology
mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X {\displaystyle
Lefschetz_fixed-point_theorem
Theorems connecting continuity to closure of graphs
noted in Open mapping theorem (functional analysis) § Statement and proof, it is enough to prove the open mapping theorem for a continuous linear operator
Closed graph theorem (functional analysis)
Closed_graph_theorem_(functional_analysis)
Theorem in probability theory
Next we apply the continuous mapping theorem, recognizing the functions g(x,y) = x + y, g(x,y) = xy, and g(x,y) = x y−1 are continuous (for the last function
Slutsky's_theorem
Theorem in mathematics
its average speed for the whole trip. The theorem states precisely that if a real-valued function is continuous on a closed interval [ a , b ] {\displaystyle
Mean_value_theorem
Notions of probabilistic convergence, applied to estimation and asymptotic analysis
notation Skorokhod's representation theorem The Tweedie convergence theorem Slutsky's theorem Continuous mapping theorem Bickel et al. 1998, A.8, page 475
Convergence of random variables
Convergence_of_random_variables
Multivariate functions can be written using univariate functions and summing
the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function f : [ 0 , 1 ] n → R {\displaystyle
Kolmogorov–Arnold representation theorem
Kolmogorov–Arnold_representation_theorem
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
Concept in topology
In topology, the degree of a continuous mapping between two compact oriented manifolds of the same dimension is a number that represents the number of
Degree of a continuous mapping
Degree_of_a_continuous_mapping
Property of artificial neural networks
universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate any continuous function to any desired
Universal approximation theorem
Universal_approximation_theorem
Theorem in mathematics
the contraction mapping theorem. For functions of a single variable, the theorem states that if f {\displaystyle f} is a continuously differentiable function
Inverse_function_theorem
Existence and uniqueness of solutions to initial value problems
known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard,
Picard–Lindelöf_theorem
Central limit theorem (probability) Clark–Ocone theorem (stochastic processes) Continuous mapping theorem (probability theory) Cramér's theorem (large deviations)
List_of_theorems
Theorem that any three objects in space can be simultaneously bisected by a plane
fraction of pancake #1 covered by the line changes continuously from 0 to 1, so by the intermediate value theorem it must be equal to 1/2 somewhere along the
Ham_sandwich_theorem
Function reducing distance between all points
and y in M. Every contraction mapping is Lipschitz continuous and hence uniformly continuous (for a Lipschitz continuous function, the constant k is no
Contraction_mapping
Mathematical function with no sudden changes
extension theorem and the Hahn–Banach theorem. If f : S → Y {\displaystyle f\colon S\to Y} is not continuous, then it could not possibly have a continuous extension
Continuous_function
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)
Mathematical function that preserves angles
conformal mappings are precisely the locally invertible complex analytic functions. In three and higher dimensions, Liouville's theorem sharply limits
Conformal_map
Markov–Kakutani fixed-point theorem, named after Andrey Markov and Shizuo Kakutani, states that a commuting family of continuous affine self-mappings of a compact convex
Markov–Kakutani fixed-point theorem
Markov–Kakutani_fixed-point_theorem
Every Riemannian manifold can be isometrically embedded into some Euclidean space
contraction mapping theorem could be applied. Given an m-dimensional Riemannian manifold (M, g), an isometric embedding is a continuously differentiable
Nash_embedding_theorems
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
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
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 in calculus relating line and double integrals
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R
Green's_theorem
Method in statistics
{\xrightarrow {P}}\,\theta } and since g′(θ) is continuous, applying the continuous mapping theorem yields g ′ ( θ ~ ) → P g ′ ( θ ) , {\displaystyle
Delta_method
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)
Theorem relating continuity to graphs
In mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each
Closed_graph_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
Mathematical theorem regarding operators
Blackwell's contraction mapping theorem provides a set of sufficient conditions for an operator to be a contraction mapping. It is widely used in areas
Blackwell's contraction mapping theorem
Blackwell's_contraction_mapping_theorem
Mapping which preserves all topological properties of a given space
{\displaystyle f} is continuous, the inverse function f − 1 {\displaystyle f^{-1}} is continuous ( f {\displaystyle f} is an open mapping). A homeomorphism
Homeomorphism
Theorem in homotopy theory
homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on
Whitehead_theorem
Theorem in topology
points. Every continuous path connecting a point of one region to a point of the other intersects with the curve somewhere. While the theorem seems intuitively
Jordan_curve_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
Mathematical transform that expresses a function of time as a function of frequency
Plancherel's and Parseval's theorem. When the function is integrable, the Fourier transform is still uniformly continuous and the Riemann–Lebesgue lemma
Fourier_transform
Theorem in mathematics and economics
we have the following theorem. Theorem: Assume that V {\displaystyle V} and L {\displaystyle {\mathcal {L}}} are continuously differentiable. Then ∂
Envelope_theorem
Theorem
functional analysis in mathematics, the Hille–Yosida theorem characterizes the generators of strongly continuous one-parameter semigroups of linear operators
Hille–Yosida_theorem
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
Theorems generalizing the Brouwer fixed-point theorem
Markov–Kakutani fixed-point theorem (1936-1938) and the Ryll-Nardzewski fixed-point theorem (1967) for continuous affine self-mappings of compact convex sets
Fixed-point theorems in infinite-dimensional spaces
Fixed-point_theorems_in_infinite-dimensional_spaces
Statement on solutions to ordinary differential equations
existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows existence
Carathéodory's existence theorem
Carathéodory's_existence_theorem
Concept in topology
mathematics, especially in algebraic topology, the mapping space between two spaces is the space of all the (continuous) maps between them. Viewing the set of all
Mapping_space
is continuous. On the other hand, the Hahn–Banach theorem, which applies to all locally convex spaces, guarantees the existence of many continuous linear
Discontinuous_linear_map
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
Area of mathematics
states that if a continuous linear operator between Banach spaces is surjective then it is an open map. More precisely, Open mapping theorem—If X {\displaystyle
Functional_analysis
Condition for a mathematical function to map some value to itself
By contrast, the Brouwer fixed-point theorem (1911) is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional
Fixed-point_theorem
Branch of functional analysis
denotes the mapping z → z on C, then: π T ( [ η + i ] − 1 ) = [ T + i ] − 1 . {\displaystyle \pi _{T}\left([\eta +i]^{-1}\right)=[T+i]^{-1}.} Theorem— Any self-adjoint
Borel_functional_calculus
Bound on eigenvalues
In mathematics, the Gershgorin circle theorem (also called sometimes Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix. It
Gershgorin_circle_theorem
On the existence of a continuous selection of a multivalued map from a paracompact space
selection theorem is a selection theorem named after Ernest Michael. In its most popular form, it states the following: Michael Selection Theorem—Let X be
Michael_selection_theorem
Frameworks for modeling variables that evolve over time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete
Discrete time and continuous time
Discrete_time_and_continuous_time
Integral criterion for holomorphy
Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a function is holomorphic. Morera's theorem states that a continuous, complex-valued
Morera's_theorem
Statistical estimator
Another useful result is the continuous mapping theorem: if Tn is consistent for θ and g(·) is a real-valued function continuous at the point θ, then g(Tn)
Consistent_estimator
Mathematical theorem in complex analysis
{\displaystyle D} . This statement can be viewed as a special case of the open mapping theorem, which states that a nonconstant holomorphic function maps open sets
Maximum_modulus_principle
R), the space of all continuous functions from the unit interval into the real line. On the one hand, the Banach–Mazur theorem seems to tell us that
Banach–Mazur_theorem
On tangency patterns of circles
higher-dimensional space is a continuous function from one set to the other that preserves the angles between any two curves. The Riemann mapping theorem, formulated by
Circle_packing_theorem
On the homology of continuous maps between compact metric spaces
The Vietoris–Begle mapping theorem is a result in the mathematical field of algebraic topology. It is named for Leopold Vietoris and Edward G. Begle.
Vietoris–Begle mapping theorem
Vietoris–Begle_mapping_theorem
Mathematical rule
cycles of a continuous mapping of the line into itself". Ukrainian Math. J. 16: 61–71. K. Burns, B. Hasselblatt, "The Sharkovsky Theorem: A Natural Direct
Sharkovskii's_theorem
Topics referred to by the same term
Continuity (disambiguation) Continuous mapping theorem This disambiguation page lists articles associated with the title Continuity theorem. If an internal link
Continuity_theorem
Study of convergence properties of statistical estimators
Central limit theorem Continuous mapping theorem Glivenko–Cantelli theorem Law of large numbers Law of the iterated logarithm Slutsky's theorem Delta method
Asymptotic theory (statistics)
Asymptotic_theory_(statistics)
Group of isotopy classes of a topological automorphism group
functions, so that we can consider continuous deformation of the homeomorphisms themselves called homotopies. We define the mapping class group by taking homotopy
Mapping_class_group
In particular, the continuous functional calculus commutates with the Gelfand representation. With the spectral mapping theorem, functions with certain
Continuous functional calculus
Continuous_functional_calculus
Type of mathematical space
every continuous real-valued function on a compact space has these properties. For compact subsets of Euclidean space, this is the extreme value theorem. Another
Compact_space
Mathematical method
selection theorems come into action: they guarantee that, if F satisfies certain properties, then it has a selection f that is continuous or has other
Selection_theorem
Integral expressing the amount of overlap of one function as it is shifted over another
\quad f\in L^{p},\ g\in L^{q},} so that the convolution is a continuous bilinear mapping from Lp×Lq to Lr. The Young inequality for convolution is also
Convolution
between any two shift spaces (that is, continuous mappings that commute with the shift) are exactly those mappings which can be defined uniformly by a local
Curtis–Hedlund–Lyndon_theorem
fixed-point theorems were developed by Iimura, Murota and Tamura, Chen and Deng and others. Yang provides a survey. Continuous fixed-point theorems often require
Discrete_fixed-point_theorem
Normed vector space that is complete
Open Mapping Theorem—Let X {\displaystyle X} and Y {\displaystyle Y} be Banach spaces and T : X → Y {\displaystyle T:X\to Y} be a surjective continuous linear
Banach_space
Theorem in quantum mechanics
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from
Gleason's_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
In mathematics, vector space of linear forms
By the Riesz–Markov–Kakutani representation theorem, the continuous dual of certain spaces of continuous functions can be described using measures. If
Dual_space
correction Continuous distribution – see Continuous probability distribution Continuous mapping theorem Continuous probability distribution Continuous stochastic
List_of_statistics_articles
Theorem in complex analysis
thus it is also continuous on its closure B ¯ ( 0 , R ) {\displaystyle {\overline {B}}(0,R)} . By the extreme value theorem, a continuous function on a
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Theorem relating unitary operators to one-parameter Lie groups
families are ordinarily referred to as strongly continuous one-parameter unitary groups. The theorem was proved by Marshall Stone (1930, 1932), and John
Stone's theorem on one-parameter unitary groups
Stone's_theorem_on_one-parameter_unitary_groups
Transformations induced by a mathematical group
known as the orbit–stabilizer theorem. If G is finite then the orbit–stabilizer theorem, together with Lagrange's theorem, gives | G ⋅ x | = [ G : G x
Group_action
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
Group that is also a differentiable manifold with group operations that are smooth
Combining these two ideas, one obtains a continuous group where multiplying points and their inverses is continuous. If the multiplication and taking of inverses
Lie_group
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
Property of functions which is weaker than continuity
{\displaystyle f_{1}\leq f_{2}\leq f_{3}\leq \cdots } of continuous functions is lower semicontinuous. (The Theorem of Baire below provides a partial converse.) The
Semi-continuity
Theorem in topology about homeomorphic subsets of Euclidean space
certain types of continuous maps from a Banach space to itself. Open mapping theorem for other conditions that ensure that a given continuous map is open.
Invariance_of_domain
Provides integral formulas for all derivatives of a holomorphic function
integral theorem, it is sufficient to require that f {\displaystyle f} be holomorphic in the open region enclosed by the path and continuous on its closure
Cauchy's_integral_formula
when its Fourier transform is continuous at zero in the Sazonov topology and such a topology is called sufficient. The theorem is named after the two Russian
Minlos–Sazonov_theorem
approximate continuous functions between topological spaces that can be triangulated; this is formalized by the simplicial approximation theorem. A simplicial
Simplicial_map
Theorem in geometry about convex sets
topological Radon theorem generalizes this formluation. It allows f to be any continuous function - not necessarily affine: If ƒ is any continuous function from
Radon's_theorem
Principle in quantum information theory
In physics, the no-communication theorem (also referred to as the no-signaling principle) is a no-go theorem in quantum information theory. It asserts
No-communication_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
Characteristic property of holomorphic functions
continuous differentiability of f need not be assumed. The hypotheses of Goursat's theorem can be weakened significantly. If f = u + iv is continuous
Cauchy–Riemann_equations
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
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
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
Earle–Hamilton fixed-point theorem
Earle–Hamilton_fixed-point_theorem
Duality for locally compact abelian groups
as the group of continuous characters, the natural pairing between a locally compact abelian group and its dual, and the duality theorem identifying a group
Pontryagin_duality
Mathematical function whose derivative exists
differentiable but not continuously differentiable (i.e., the derivative is not a continuous function). Nevertheless, Darboux's theorem implies that the derivative
Differentiable_function
Characterization of surjectivity
surjective. The importance of this theorem is related to the open mapping theorem, which states that a continuous linear surjection between Fréchet spaces
Surjection_of_Fréchet_spaces
Curve whose range contains the unit square
{\displaystyle g} is a continuous function mapping the Cantor set onto the entire unit square. (Alternatively, we could use the theorem that every compact
Space-filling_curve
CONTINUOUS MAPPING-THEOREM
CONTINUOUS MAPPING-THEOREM
Boy/Male
Hindu, Indian, Marathi
Continuous Extended
Boy/Male
Gujarati, Hindu, Indian, Marathi, Sanskrit
Continuous; Ongoing
Girl/Female
Hindu, Indian
Continuous
Girl/Female
Tamil
Continuous, Younger sister
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.
Girl/Female
Hindu, Indian, Marathi, Tamil, Telugu
Continuous Flow
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 and Irish
English and Irish : probably a hypercorrected form of Lappin.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Continuous
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).
Boy/Male
Gujarati, Hindu, Indian
Continuous
Boy/Male
Hindu
Continuous
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Continuous
Surname or Lastname
English (Devon)
English (Devon) : variant spelling of Appling.
Boy/Male
Tamil
Continuous
Girl/Female
Indian
Continuous, Younger sister
Boy/Male
Tamil
Continuous
Boy/Male
Tamil
Continuous
Girl/Female
Indian
Continuous, Younger sister
Girl/Female
Tamil
Continuous, Younger sister
CONTINUOUS MAPPING-THEOREM
CONTINUOUS MAPPING-THEOREM
Boy/Male
British, English
From the Island of Linden Trees
Girl/Female
Indian
Honey Bee
Boy/Male
Hindu
Boy/Male
Indian, Punjabi, Sikh
Light of the Intellect
Boy/Male
Tamil
Rohanlal | ரோஹநலால
Lord Krishna
Boy/Male
Australian, German, Teutonic
Hard-working Ruler; Home Ruler
Girl/Female
Indian
She was a literary woman and a poetess in qastaniniyah
Girl/Female
Hindu
Girl/Female
Hindu
Wonderment, Amazement, Wondering
Female
English
Variant spelling of English Abigail, ABBIGAEL means "father rejoices."
CONTINUOUS MAPPING-THEOREM
CONTINUOUS MAPPING-THEOREM
CONTINUOUS MAPPING-THEOREM
CONTINUOUS MAPPING-THEOREM
CONTINUOUS MAPPING-THEOREM
a.
Not deviating or varying from uninformity; not interrupted; not joined or articulated.
n.
A kind of machine blanket or wrapping material used by calico printers.
a.
Without break, cessation, or interruption; without intervening space or time; uninterrupted; unbroken; continual; unceasing; constant; continued; protracted; extended; as, a continuous line of railroad; a continuous current of electricity.
n.
A continuous fever.
a.
Biting; pinching; painful; destructive; as, a nipping frost; a nipping wind.
n.
Thread; continuous line.
a.
Not continuous; interrupted; broken off.
adv.
In a continuous maner; without interruption.
a.
Pertaining to the harp; as, harping symphonies.
n.
Basso continuo, or continued bass.
p. pr. & vb. n.
of Map
a.
Contiguous.
a.
Contiguous; touching.
n.
Continuous growth; an accretion.
a.
Contiguous.
n.
A continuous noise or murmur.
n.
The process of cleaning or brightening sheet metal or metalware, esp. brass, by dipping it in acids, etc.
n.
The act of one who, or that which, marks; the mark or marks made; arrangement or disposition of marks or coloring; as, the marking of a bird's plumage.
a.
In actual contact; touching; also, adjacent; near; neighboring; adjoining.
n.
The process of making, or of becoming malt.