of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to...
25 KB (3,426 words) - 18:24, 14 March 2025
In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures...
103 KB (13,457 words) - 12:16, 1 May 2025
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...
14 KB (1,935 words) - 21:24, 26 June 2025
convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can...
58 KB (10,541 words) - 04:52, 2 July 2025
put it more abstractly every seminormed vector space is a topological vector space and thus carries a topological structure which is induced by the semi-norm...
18 KB (2,881 words) - 18:43, 8 May 2025
spaces Bounded set (topological vector space) – Generalization of boundedness PlanetMath entry for Locally Bounded nLab entry for Locally Bounded Category...
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operator theory, a bounded linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological vector spaces (TVSs) X {\displaystyle...
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implies that a convex set in a real or complex topological vector space is path-connected (and therefore also connected). A set C is strictly convex if...
27 KB (3,429 words) - 17:52, 10 May 2025
analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get...
91 KB (15,850 words) - 22:49, 28 June 2025
be called the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear...
45 KB (6,865 words) - 17:01, 9 July 2025
ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations...
23 KB (3,947 words) - 05:47, 21 May 2025
claimed to be homeomorphic to the topological quotient. Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback...
82 KB (11,434 words) - 17:46, 21 May 2025
Metacompact space Noetherian topological space Orthocompact space Paracompact space Quasi-compact morphism Precompact set - also called totally bounded Relatively...
45 KB (5,704 words) - 04:39, 27 June 2025
Look up bounded in Wiktionary, the free dictionary. Boundedness, bounded, or unbounded may refer to: Bounded rationality, the idea that human rationality...
2 KB (316 words) - 11:29, 13 September 2024
Seminorm (redirect from Locally bounded topological vector space)
and only if it is a T1 space). A locally bounded topological vector space is a topological vector space that possesses a bounded neighborhood of the origin...
32 KB (6,145 words) - 15:28, 13 May 2025
if it is complete as a topological vector space. If ( X , τ ) {\displaystyle (X,\tau )} is a metrizable topological vector space (such as any norm induced...
102 KB (17,019 words) - 16:58, 14 April 2025
theorem. In topological vector spaces, a different definition for bounded sets exists which is sometimes called von Neumann boundedness. If the topology...
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inherited by the function space. For example, the set of functions from any set X into a vector space has a natural vector space structure given by pointwise...
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In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied...
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principal topological properties that distinguish topological spaces. A subset of a topological space X {\displaystyle X} is a connected set if it is a...
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absolutely convex hull of a bounded set in a locally convex topological vector space is again bounded. If D {\displaystyle D} is a bounded disk in a TVS X {\displaystyle...
11 KB (1,913 words) - 09:38, 28 August 2024
analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order...
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bilinear form Topological vector space, a blend of topological structure with the algebraic concept of a vector space A vector field is a vector-valued function...
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Absolutely convex set – Convex and balanced set Absorbing set – Set that can be "inflated" to reach any point Bounded set (topological vector space) – Generalization...
27 KB (5,279 words) - 16:57, 21 March 2024
set Balanced set – Construct in functional analysis Bornivorous set – A set that can absorb any bounded subset Bounded set (topological vector space) –...
40 KB (7,720 words) - 21:39, 22 May 2024
Riesz (Riesz 1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role...
65 KB (12,204 words) - 16:12, 8 July 2025
mathematics known as functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from X {\displaystyle...
39 KB (6,393 words) - 20:06, 12 September 2024
bounded subset Bounded set (topological vector space) – Generalization of boundedness Locally convex topological vector space – Vector space with a topology...
26 KB (3,804 words) - 18:56, 27 December 2023
pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). An LM-space is an inductive limit...
64 KB (10,603 words) - 20:30, 8 January 2025
and topological structures underlie the linear topological space (in other words, topological vector space) structure. A linear topological space is both...
69 KB (9,328 words) - 07:59, 25 June 2025