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.
References in periodicals archive ?
Seoane-Sepulveda, Linear subsets of nonlinear sets in topological vector spaces, Bull.
The more general case when E is a topological vector space will be presented in Remark 2.
Let E be a topological vector space and B an absolutely convex, closed and bounded, subset of E.
Let E be a normal topological vector space, Y a topological vector space, U an open subset of E, L : dom L [subset or equal to] E [PHI] Y a linear single valued map and T [member of] [H.
Let X be a nonempty subset of a topological vector space and f: X x X [right arrow] R be a function with f{x, x) [greater than or equal to] 0 for all x [member ] X.
Let X be a topological vector space and T : X [right arrow] X an operator.
Modern methods in topological vector spaces (reprint, 1978).
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.
Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.
O'Regan, Fixed point theory for set valued mappings between topological vector spaces having sufficiently many linear functionals, Computers and Mathematics with Applications 41 (2001), 917-928.