• 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...
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    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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  • 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
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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
  • pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). An LM-space is an inductive limit...
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  • 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...
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    claimed to be homeomorphic to the topological quotient. Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback...
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    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...
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    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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    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
  • 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...
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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...
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  • 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...
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  • Look up bounded in Wiktionary, the free dictionary. Boundedness, bounded, or unbounded may refer to: Bounded rationality, the idea that human rationality...
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  • Thumbnail for Vector space
    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...
    89 KB (11,804 words) - 06:15, 9 July 2025
  • 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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  • 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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    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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  • 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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  • 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
  • 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) –...
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  • bounded subset Bounded set (topological vector space) – Generalization of boundedness Locally convex topological vector space – Vector space with a topology...
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  • Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that...
    29 KB (4,998 words) - 23:19, 9 May 2025
  • and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms...
    17 KB (2,443 words) - 19:09, 4 May 2025