# topological vector space

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## topological vector space

[‚täp·ə¦läj·ə·kəl ′vek·tər ‚spās]
(mathematics)
A vector space which has a topology with the property that vector addition and scalar multiplication are continuous functions. Also known as linear topological space; topological linear space.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
He said the theme of the conference will cover the major areas of mathematical sciences, such as Functional Analysis and its Applications, Fluid Dynamics, Fuzzy logic, Topological Vector Spaces and Nonlinear Operator Theory, Best Approximations Theory, Soft Set Theory, Graph Theory, Algebra and so on.
He added that the theme of the conference will cover the major areas of Mathematical sciences such as; Functional Analysis and its Applications, Fluid Dynamics, Fuzzy logic, Topological Vector Spaces and Nonlinear Operator Theory, Best Approximations Theory, Soft Set Theory, Graph Theory, Algebra and more.
Morris, "Embedding into free topological vector spaces on compact metrizable spaces," Topology and its Applications, vol.
The upper semi- continuity related to topological vector spaces are extended to upper demicontinuity, to upper hemicontinuity, and to generalized upper hemicontinuity.
The study of lineability (and other properties of subsets of topological vector spaces, together with the type of algebraic structure to be considered) tries to generalize the existence of those elements fulfilling pathological properties through finding large algebraic structures of such examples.
Fuzzy vector spaces and fuzzy topological vector spaces. Journal of Mathematical Analysis and Applications, v.
Modern methods in topological vector spaces (reprint, 1978).
The next result extends Proposition 3.1 of [10] from normed linear spaces to metrizable topological vector spaces.
Because each PN space is a [T.sub.2] space, so (R, [v.sub.1], [[tau].sub.1], [[tau].sub.1.sup.*]) is LS equivalent to (R, [v.sub.2], [[tau].sub.2], [[tau].sub.2.sup.*]) when they are all topological vector spaces. Combining with Lemma 4.9 and Lemma 4.
Schaeffer: Topological Vector Spaces, Springer Verlag, 1986.
They write for students who are familiar with general topology and linear algebra, but not topological vector spaces. Among the topics are commutative topological groups, locally convex spaces and semi-norms, Hahn-Banach theorems, barreled spaces, closed graph theorems, and reflexivity.
Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.

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