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Collection of mathematical objects of finite size
(M, d) is a bounded metric space (or d is a bounded metric) if M is bounded as a subset of itself. Total boundedness implies boundedness. For subsets
Bounded_set
Mathematical function whose set of values is bounded
is bounded. (However, a continuous function must be bounded if its domain is both closed and bounded.) Bounded set Compact support Local boundedness Uniform
Bounded_function
Generalization of compactness
mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered
Totally_bounded_space
Generalization of boundedness
analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector
Bounded set (topological vector space)
Bounded_set_(topological_vector_space)
Fractal named after mathematician Benoit Mandelbrot
) ) {\displaystyle f_{c}(f_{c}(0))} , and so on, remains bounded in absolute value. This set was first defined and drawn by Robert W. Brooks and Peter
Mandelbrot_set
Majorant and minorant in mathematics
lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below)
Upper_and_lower_bounds
Function between topological vector spaces
is bounded. Function bounded on a neighborhood and local boundedness In contrast, a map F : X → Y {\displaystyle F:X\to Y} is said to be bounded on a
Continuous_linear_operator
function is locally bounded if it is bounded around every point. A family[disambiguation needed] of functions is locally bounded if for any point in their
Local_boundedness
Set theory concept
In mathematics, particularly in mathematical logic and set theory, a club set is a subset of a limit ordinal that is closed under the order topology, and
Club_set
Mathematical generalization of boundedness
and the other is to study notions related to boundedness (vector bornologies, bounded operators, bounded subsets, etc.). For normed spaces, from which
Bornology
Kind of linear transformation
ensure that bounded sets remain bounded: a bounded linear operator is thus a linear transformation that sends bounded sets to bounded sets. Formally, it
Bounded_operator
Concept in geometry and topology
inverse images of small open sets, or neighborhoods, are themselves open. Large-scale properties of a space—such as boundedness, or the degrees of freedom
Coarse_structure
Vector space with a partial order
{\displaystyle X} that map every order interval into a bounded set is called the order bound dual of X {\displaystyle X} and denoted by X b . {\displaystyle
Ordered_vector_space
Subset of Euclidean space is compact if and only if it is closed and bounded
Heine–Borel property (R.E. Edwards uses the term boundedly compact space) if each closed bounded set in X {\displaystyle X} is compact. No infinite-dimensional
Heine–Borel_theorem
Largest distance between two points
lesion or in geology concerning a rock. A bounded set is a set whose diameter is finite. Within a bounded set, all distances are at most the diameter.
Diameter_of_a_set
Vector space with a notion of nearness
definition of boundedness can be weakened a bit; E {\displaystyle E} is bounded if and only if every countable subset of it is bounded. A set is bounded if and
Topological_vector_space
Type of continuous linear operator
finite-dimensional behavior by sending bounded sets to sets whose closures are compact, or equivalently, in normed spaces, by sending bounded sequences to sequences with
Compact_operator
Logical quantification that ranges over a subset of the universe of discourse
"∃". Bounded quantifiers differ from "∀" and "∃" in that bounded quantifiers restrict the range of the quantified variable. The study of bounded quantifiers
Bounded_quantifier
Real-valued function
mathematics, a function of bounded mean oscillation, also known as a BMO function, is a real-valued function whose mean oscillation is bounded (finite). The space
Bounded_mean_oscillation
Making of satisfactory, not optimal, decisions
approach to increase their utility. In addition to bounded rationality, bounded willpower and bounded selfishness are two other key concepts in behavioral
Bounded_rationality
Convex hull of a finite set of points in a Euclidean space
polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue.
Convex_polytope
Real function with finite total variation
analysis, a function of bounded variation, also known as BV function, is a real-valued function whose total variation is bounded (finite): the graph of
Bounded_variation
Topics referred to by the same term
Precompact set may refer to: Relatively compact subspace, a subset whose closure is compact Totally bounded set, a subset that can be covered by finitely
Precompact_set
Topics referred to by the same term
Look up bounded in Wiktionary, the free dictionary. Boundedness, bounded, or unbounded may refer to: Bounded rationality, the idea that human rationality
Boundedness
Order whose elements are all comparable
is complete if and only if every bounded set that is closed in the order topology is compact. A totally ordered set (with its order topology) which is
Total_order
Family of graphs whose shallow minors are sparse graphs
is said to have bounded expansion if all of its shallow minors are sparse graphs. Many natural families of sparse graphs have bounded expansion. A closely
Bounded_expansion
In geometry, set whose intersection with every line is a single line segment
to take convex combinations of points. Absorbing set Algorithmic problems on convex sets Bounded set (topological vector space) Brouwer fixed-point theorem
Convex_set
Set that can absorb any bounded subset
locally bounded (i.e. maps bounded sets to bounded sets). A linear map between two TVSs is called infrabounded if it maps Banach disks to bounded disks
Bornivorous_set
dense set Bounded set Totally bounded set Borel set Baire set Measurable set, Non-measurable set Universally measurable set Negligible set Null set Haar
List_of_types_of_sets
Extended measure of size in mathematics
bounded open set is not necessarily Jordan measurable. For example, the complement of the fat Cantor set (within the interval) is not. A bounded set is
Peano–Jordan_measure
obtained by requiring that quantifiers be bounded in the induction axiom or equivalent postulates (a bounded quantifier is of the form ∀x ≤ t or ∃x ≤ t
Bounded_arithmetic
Topics referred to by the same term
closed and bounded sets in Rn The Weierstrass extreme value theorem, which states that a continuous function on a closed and bounded set obtains its
Weierstrass_theorem
High-area shapes can shift to hold many grid points
mathematical theorem in the geometry of numbers, stating that whenever a bounded set in the Euclidean plane has area A {\displaystyle A} , it can be translated
Blichfeldt's_theorem
{\displaystyle \chi } -boundedness is a nontrivial concept, true for some graph families and false for others. Every class of graphs of bounded chromatic number
Chi-bounded
Measure of the "size" of linear operators
of a bounded set under a continuous operator is also bounded. Because of this property, the continuous linear operators are also known as bounded operators
Operator_norm
Mathematical space with a notion of distance
of a metric space that is bounded but not totally bounded is R 2 {\displaystyle \mathbb {R} ^{2}} (or any other infinite set) with the discrete metric
Metric_space
Convex and balanced set
Balanced set – Construct in functional analysis Bounded set (topological vector space) – Generalization of boundedness Convex set – In geometry, set whose
Absolutely_convex_set
{\displaystyle 1} , respectively. Bounded lattices are of considerable importance because many algebraic structures are bounded lattices, including complete
Bounded_lattice
von Neumann architecture von Neumann bicommutant theorem von Neumann bounded set Von Neumann bottleneck von Neumann cardinal assignment von Neumann cellular
List of things named after John von Neumann
List_of_things_named_after_John_von_Neumann
Type of mathematical space
of the set. Likewise, whereas every real-valued function on a finite set is bounded and attains its maximum and minimum, every continuous real-valued function
Compact_space
Space where bounded operators are continuous
generalization of boundedness Bornivorous set – Set that can absorb any bounded subset Bounded set (topological vector space) – Generalization of boundedness Locally
Bornological_space
Initial set of valid possible values
set. In this case the problem has no solution and is said to be infeasible. Feasible sets may be bounded or unbounded. For example, the feasible set defined
Feasible_region
Construct in functional analysis
of a compact (respectively, totally bounded, bounded) set has the same property. The convex hull of a balanced set is convex and balanced (that is, it
Balanced_set
All numbers between two given numbers
Bounded intervals are also commonly known as finite intervals. Bounded intervals are bounded sets, in the sense that their diameter (which is equal to the absolute
Interval_(mathematics)
Type of vector space in math
Every weakly convergent sequence {xn} is bounded, by the uniform boundedness principle. Conversely, every bounded sequence in a Hilbert space admits weakly
Hilbert_space
Sequences of convex sets in a bounded set have convergent subsequences
sequences of convex sets. Specifically, given a sequence { K n } {\displaystyle \{K_{n}\}} of convex sets contained in a bounded set, the theorem guarantees
Blaschke_selection_theorem
Method for the construction of fractals
compact (closed and bounded) fixed set S. One way of constructing a fixed set is to start with an initial nonempty closed and bounded set S0 and iterate the
Iterated_function_system
Open cover in mathematical analysis
dimension N with the following property: Given any Besicovitch cover F of a bounded set E, there are cN subcollections of balls A1 = {Bn1}, …, AcN = {BncN} contained
Besicovitch_covering_theorem
Continuous real function on a closed interval has a maximum and a minimum
Theorem By the boundedness theorem, f is bounded from above, hence, by the Dedekind-completeness of the real numbers, the least upper bound (supremum) M
Extreme_value_theorem
Closed volume that completely contains the union of a set of objects
be non-empty and bounded (finite). Bounding volumes are most often used to accelerate certain kinds of tests. In ray tracing, bounding volumes are used
Bounding_volume
Point not between two other points
Banach space with the Radon–Nikodym property, a nonempty closed and bounded set has an extreme point. (In infinite-dimensional spaces, the property of
Extreme_point
Type of convergence in Hilbert spaces
convex bounded closed set is weakly compact. As a consequence of the principle of uniform boundedness, every weakly convergent sequence is bounded. The
Weak convergence (Hilbert space)
Weak_convergence_(Hilbert_space)
all i {\displaystyle i} are bounded), A f , r {\displaystyle A_{f,r}} is bounded. One can define the rectangular bounding box A ~ f , r {\displaystyle
Ratio_of_uniforms
Smallest box which encloses some set of points
the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set S in N dimensions
Minimum_bounding_box
Topological vector space whose topology can be defined by a metric
there exists a countable set B {\displaystyle {\mathcal {B}}} of bounded subsets of X {\displaystyle X} such that every bounded subset of X {\displaystyle
Metrizable topological vector space
Metrizable_topological_vector_space
Property of a partially ordered set
partially ordered set X has the least-upper-bound property if every non-empty subset of X with an upper bound has a least upper bound (supremum) in X.
Least-upper-bound_property
on F {\displaystyle F} is Hausdorff. Boundedness A subset H {\displaystyle H} of F {\displaystyle F} is bounded in the G {\displaystyle {\mathcal {G}}}
Topologies on spaces of linear maps
Topologies_on_spaces_of_linear_maps
compact invariant set that attracts all bounded deterministic sets. If a random dynamical system has a compact random absorbing set K {\displaystyle K}
Pullback_attractor
Branch of mathematics that studies sets
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any
Set_theory
Extension of the Brouwer fixed-point theorem
the set { x ∈ X : x = λ f ( x ) for some 0 ≤ λ ≤ 1 } {\displaystyle \{x\in X:x=\lambda f(x){\mbox{ for some }}0\leq \lambda \leq 1\}} is bounded. Then
Schauder_fixed-point_theorem
Subset of a topological space whose closure is compact
relatively compact set. This needs to be made precise in terms of the topology used, in a particular theory. Compactly embedded Totally bounded space page 12
Relatively_compact_subspace
Dual space topology of uniform convergence on some sub-collection of bounded subsets
( X , Y , b ) − bounded subset of X } . {\displaystyle \left\{A^{\circ }~:~A\subseteq X{\text{ is a }}\sigma (X,Y,b)-{\text{bounded}}{\text{ subset
Polar_topology
Method of determining fractal dimension
box-counting dimension, is a way of determining the fractal dimension of a bounded set S {\textstyle S} in a Euclidean space R n {\textstyle \mathbb {R} ^{n}}
Minkowski–Bouligand_dimension
Continuous dual space endowed with the topology of uniform convergence on bounded sets
there exists a countable set B {\displaystyle {\mathcal {B}}} of bounded subsets of X {\displaystyle X} such that every bounded subset of X {\displaystyle
Strong_dual_space
Property of group subsets (mathematics)
Balanced set – Construct in functional analysis Bounded set (topological vector space) – Generalization of boundedness Convex set – In geometry, set whose
Symmetric_set
Feature of certain mathematical spaces
operator: any bounded set in X {\displaystyle X} is totally bounded in Y {\displaystyle Y} , i.e. every sequence in such a bounded set has a subsequence
Compact_embedding
Type of continuity of a complex-valued function
\|\cdot \|_{C^{k,\alpha }}} . Let Ω be a bounded subset of some Euclidean space (or more generally, any totally bounded metric space) and let 0 < α < β ≤ 1
Hölder_condition
Consumer preferences property
if the consumption set is unbounded or open (in other words, it is not compact) or if x is on a section of a bounded consumption set sufficiently far away
Local_nonsatiation
Concept in communication theory
employee's home life. Bounded emotionality was proposed by Dennis K. Mumby and Linda Putnam. Mumby and Putnam (1992) stress that bounded emotionality encourages
Bounded_emotionality
{\displaystyle A\times A\to A} ), or stereotype continuity: for each totally bounded set S ⊆ A {\displaystyle S\subseteq A} and for each neighbourhood of zero
Topological_algebra
In Euclidean space, a measure of that set's "size"
^{n}} , n ≥ 3; K will denote the n-dimensional compact (i.e., closed and bounded) set of which Σ is the boundary. Let S be another (n − 1)-dimensional hypersurface
Capacity_of_a_set
Set of points touching all convex bodies of unit volume
Does a Danzer set with bounded density or bounded separation exist? More unsolved problems in mathematics In geometry, a Danzer set is a set of points that
Danzer_set
Construction in functional analysis, useful to solve differential equations
h: S → C is called essentially bounded if h is bounded μ-almost everywhere. An essentially bounded h induces a bounded multiplication operator Th on Lp(μ):
Decomposition of spectrum (functional analysis)
Decomposition_of_spectrum_(functional_analysis)
Sphere that contains a set of objects
given a non-empty set of objects of finite extension in d {\displaystyle d} -dimensional space, for example a set of points, a bounding sphere, enclosing
Bounding_sphere
finite radius. A function taking values in a metric space is bounded if its image is a bounded set. Category of topological spaces The category Top has topological
Glossary_of_general_topology
On decreasing nested sequences of non-empty compact sets
closed). Then set S = C 1 {\displaystyle S=C_{1}} . The theorem in real analysis draws the same conclusion for closed and bounded subsets of the set of real
Cantor's_intersection_theorem
Property of point sets in Euclidean spaces
Construct in functional analysis Bounded set (topological vector space) – Generalization of boundedness Convex set – In geometry, set whose intersection with every
Star_domain
Basic integral in elementary calculus
Moreover, a function f defined on a bounded interval is Riemann-integrable if and only if it is bounded and the set of points where f is discontinuous
Riemann_integral
following: a bounded set can be covered by a single ball of some radius. Sometimes several balls of a smaller radius can also cover the set. A compact set in fact
Measure_of_non-compactness
Smallest convex set containing a given set
Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may
Convex_hull
Collection of mathematical objects
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects:
Set_(mathematics)
center of a bounded set Q {\displaystyle Q} having non-empty interior is the center of the minimal-radius ball enclosing the entire set Q {\displaystyle
Chebyshev_center
Weak topology on function spaces
operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space H {\displaystyle H} , such that the functional
Weak_operator_topology
{\displaystyle S} . If the set { x 1 , x 2 , … } {\displaystyle \left\{x_{1},x_{2},\ldots \right\}} is a (von Neumann) bounded set then the series called
Convex_series
Greatest lower bound and least upper bound
that any bounded nonempty subset S {\displaystyle S} of the real numbers has an infimum and a supremum. If S {\displaystyle S} is not bounded below, one
Infimum_and_supremum
Family of subsets representing "large" sets
{\displaystyle \mathbb {R} ^{n}} , the co-bounded subsets of X {\displaystyle X} (those whose complement is bounded set) form a filter on X {\displaystyle X}
Filter_on_a_set
set (P, ≤) is bounded complete if the following holds for any subset S of P: If S has some upper bound, then it also has a least upper bound. Bounded
Bounded_complete_poset
Axiomatic set theories based on the principles of mathematical constructivism
a decidable, inhabited set, validity of pseudo-boundedness, together with the counting sequence defined above, grants a bound for all the elements of
Constructive_set_theory
Volume space bounded by a sphere
is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the planar region bounded by
Ball_(mathematics)
Set whose pairs have minima and maxima
be embedded into a bounded lattice by adding a greatest and a least element. Furthermore, every non-empty finite lattice is bounded, by taking the join
Lattice_(order)
theory. They naturally arise from restrictions of (mixed) Poisson processes bounded intervals. Let P {\displaystyle P} be a probability distribution and let
Mixed_binomial_process
Theorem stating that pointwise boundedness implies uniform boundedness
operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The
Uniform_boundedness_principle
Theory in human biology
lower end of the range set by evolutionary pressure due to the risk of starvation if too much weight is lost and the upper bound set by pressure due to increased
Set_point_theory
Theorem that any three objects in space can be simultaneously bisected by a plane
of such hyperplanes contains at least one hyperplane that bisects the bounded set An: at one extreme translation, no volume of An is on the positive side
Ham_sandwich_theorem
starting at z. Then αs + t = αs ∘ αt and h ∘ αt = h − t. Moreover, by boundedness, d(αt(u),αt(v)) ≤ d(u,v). The flow αs can be used to transport this result
Busemann_function
Mathematical ordering with upper bounds
mathematics, a directed set (or a directed preorder or a filtered set) is a preordered set in which every finite subset has an upper bound. In other words, it
Directed_set
Region with boundary of finite measure
bounded. Therefore, a Caccioppoli set has a characteristic function whose total variation is locally bounded. From the theory of functions of bounded
Caccioppoli_set
Property of functions
In mathematics, a uniformly bounded family of functions is a family of bounded functions that can all be bounded by the same constant. This constant is
Uniform_boundedness
function of bounded deformation is a function whose distributional derivatives are not quite well-behaved-enough to qualify as functions of bounded variation
Bounded_deformation
or a bounded variation is a function with bounded total variation. Calderón Calderón–Zygmund lemma Cantor Cantor set. capacity Capacity of a set is a
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
BOUNDED SET
BOUNDED SET
Boy/Male
Hindu, Indian
Unbounded
Girl/Female
German, Swedish
Rounded; Polished Smooth
Boy/Male
Tamil
All rounder
Surname or Lastname
English
English : probably a nickname from Middle English blonde(n) ‘blond’, ‘fair-haired’.
Surname or Lastname
English
English : patronymic from Bond.
Boy/Male
Hindu
All rounder
Surname or Lastname
English
English : probably a variant of Bouldin or possibly of Bolden or Boldon.English : Alternatively, it may be a habitational name from a place in Shropshire called Bouldon.
Girl/Female
Assamese, Indian
Rounded
Boy/Male
Hindu
Unbounded
Boy/Male
Hindu
Unbounded
Boy/Male
Norse
Horn sounded for Ragnorok.
Boy/Male
Tamil
Nissim | நிஸà¯à®¸à¯€à®®
Unbounded
Nissim | நிஸà¯à®¸à¯€à®®
Boy/Male
Tamil
Unbounded
Boy/Male
Gujarati, Hindu, Indian, Kannada, Telugu
Bounded
Male
Egyptian
, Mendes.
Surname or Lastname
English
English : variant of Bond
Boy/Male
English
Man of the land.
Surname or Lastname
English
English : variant spelling of Bond.Scandinavian : status name for a farmer, from Old Norse bóndi ‘farmer’. Compare Bond. In Sweden Bonde is both a personal name and the name of an old aristocratic family.Norwegian : habitational name from a farmstead named Bonde, from Old Norse bóndi ‘farmer’ + vin ‘meadow’.
Surname or Lastname
English (Nottingham)
English (Nottingham) : variant of Pound, with the addition of the habitational or agent suffix -er.Probably a translation of South German Pfunder, Pfünder, occupational names for a weigh master or wholesaler, variants of Pfund with the addition of the agent suffix -er.
Surname or Lastname
English
English : variant of Bond.
BOUNDED SET
BOUNDED SET
Boy/Male
Australian, Bengali, Indian
God Gift; Way; Speed; Path
Girl/Female
Hindu, Indian, Sanskrit
Mother
Boy/Male
Indian, Punjabi, Sikh
Elixir of Compassion
Girl/Female
Tamil
Dancer
Boy/Male
Hindu
Courageous, Brave warrior
Surname or Lastname
English
English : variant spelling of Harrop.
Girl/Female
Tamil
Srimayee | à®·à¯à®°à¯€à®®à®¾à®¯à¯€Â
Goddess Lakshmi
Girl/Female
Latin Greek
Daughter of Cebren.
Girl/Female
Christian & English(British/American/Australian)
Spear Maiden
Boy/Male
Hindu
With strength of diamond, Lord Hanuman
BOUNDED SET
BOUNDED SET
BOUNDED SET
BOUNDED SET
BOUNDED SET
n.
Bluster; brag; untruthful boasting; audacious exaggeration; an impudent lie; a bouncer.
n.
An inflammatory fever of the body, or acute rheumatism; as, chest founder. See Chest ffounder.
v. t.
To cause to bound or rebound; sometimes, to toss.
v. i.
To make a gross error or mistake; as, to blunder in writing or preparing a medical prescription.
a.
Furnished with claws or talons; as, the pounced young of the eagle.
n.
One who places goods under bond or in a bonded warehouse.
a.
Seated or serving on horseback or similarly; as, mounted police; mounted infantry.
v. t.
To cause to blunder.
n.
A sudden leap or bound; a rebound.
p. p & a.
Bound; fastened by bonds.
imp. & p. p.
of Bounce
p. p & a.
Under obligation; bound by some favor rendered; obliged; beholden.
n.
A mass of any rock, whether rounded or not, that has been transported by natural agencies from its native bed. See Drift.
imp. & p. p.
of Bound
n.
One who bounces; a large, heavy person who makes much noise in moving.
a.
Having no bound or limit; as, unbounded space; an, unbounded ambition.
a.
Wounded to the heart with love or grief.
a.
Placed on a suitable support, or fixed in a setting; as, a mounted gun; a mounted map; a mounted gem.
v. i.
To leap or spring suddenly or unceremoniously; to bound; as, she bounced into the room.
n.
A large stone, worn smooth or rounded by the action of water; a large pebble.