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1. Topological vector space: 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 investigated in functional analysis. A topological vector space is a vector space that is ... (Vector space with a notion of nearness) [100%] 2023-12-28 [Articles containing proofs] [Topology of function spaces]...
2. Topological vector space: over a topological field $ K $ A vector space $ E $ over $ K $ equipped with a topology (cf. Topological structure (topology)) that is compatible with the vector space structure, that is, the following axioms are satisfied: 1) the mapping $ ( x _ {1 ... (Mathematics) [100%] 2023-10-18
3. Topological vector space: 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 investigated in functional analysis. A topological vector space is a vector space that is ... (Vector space with a notion of nearness) [100%] 2024-01-12 [Articles containing proofs] [Topology of function spaces]...
4. Complete topological vector space: In functional analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively closer to each other, then there exists some point \displaystyle{ x }[/math] towards ... (A TVS where points that get progressively closer to each other will always converge to a point) [86%] 2023-12-03 [Functional analysis] [Topological vector spaces]...
5. Complete topological vector space: In functional analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively closer to each other, then there exists some point x {\displaystyle x} towards ... (A TVS where points that get progressively closer to each other will always converge to a point) [86%] 2021-12-22 [Topological vector spaces]
6. Metrizable topological vector space: In functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. (A topological vector space whose topology can be defined by a metric) [86%] 2021-12-21 [Topological vector spaces]
7. Ordered topological vector space: In mathematics, specifically in functional 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 ≤ making it into an ordered vector space whose positive ... [86%] 2024-03-21 [Functional analysis] [Order theory]...
8. Topological space: A topological space is a pair (X, T), where X is a set, and T is a collection of subsets of X that satisfy the following 3 axioms: Elements in T are called "open sets". [81%] 2023-06-28 [Topology]
9. Topological space: A totality of two elements: A set $X$, consisting of elements of an arbitrary nature, called points of the given space, and a topological structure, or topology, on this set $X$ (cf. Topological structure (topology)); it is immaterial whether this ... (Mathematics) [81%] 2023-10-25
10. Topological space: In mathematics, a topological space is an ordered pair ( X , T ) {\displaystyle (X,{\mathcal {T}})} where X {\displaystyle X} is a set and T {\displaystyle {\mathcal {T}}} is a certain collection of subsets of X {\displaystyle X} called the open ... [81%] 2023-06-30
11. Topological space: In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with ... (Mathematical space with a notion of closeness) [81%] 2024-01-12 [General topology] [Topological spaces]...
12. Vector spaces: If the reader is familiar with analytic geometry, she will probably know that points in the plane can be identified by ordered tuples ( x , y ) {\displaystyle {\begin{aligned}(x,y)\end{aligned}}} where each entry is a number denoting the ... [79%] 2023-12-28 [Mathematics]
13. Locally convex topological vector space: In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can be defined as topological vector spaces whose topology is ... (A vector space with a topology defined by convex open sets) [77%] 2023-07-12 [Convex analysis] [Functional analysis]...
14. Topological vector lattice: In mathematics, specifically in functional analysis and order theory, a topological vector lattice is a Hausdorff topological vector space (TVS) \displaystyle{ X }[/math] that has a partial order \displaystyle{ \,\leq\, }[/math] making it into vector lattice that is possesses a ... [74%] 2023-06-10 [Functional analysis]
15. Vector space: A vector space, also known as a linear space, is an abstract mathematical construct with many important applications in the natural sciences, in particular in physics and numerous areas of mathematics. Some vector spaces make sense somewhat intuitively, such as ... [72%] 2023-08-17
16. Vector space: In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex ... (Algebraic structure in linear algebra) [72%] 2023-12-28 [Concepts in physics] [Group theory]...
17. Vector space: In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex ... (Algebraic structure in linear algebra) [72%] 2023-12-28 [Concepts in physics] [Group theory]...
18. Vector space: A vector space is a set of objects that can be added together and multiplied by elements of another set, while satisfying certain properties. Elements of the first set are called "vectors" while elements of the second set are called ... [72%] 2023-02-08 [Mathematics] [Algebra]...
19. Vector space: Linear space, over a field $K$ An Abelian group $E$, written additively, in which a multiplication of the elements by scalars is defined, i.e. a mapping \begin{equation} K\times E\rightarrow E\colon (\lambda,x)\rightarrow \lambda x ... (Mathematics) [72%] 2023-10-27
20. Measure in a topological vector space: A term used to designate a measure given in a topological vector space when one wishes to stress those properties of the measure that are connected with the linear and topological structure of this space. A general problem encountered in ... (Mathematics) [70%] 2022-11-19