A vector space that possesses a norm which allows computation of vector length and distance between vectors and that is complete in the sense that Cauchy sequences converge.

Baire space | barrelled space | bornological space | compactly generated space | complete space | convenient space | Fréchet space | F-space | locally complete space | locally convex space | Mackey space | metrizable space | normed space | pseudo-complete space | pseudo-metrizable space | quasi-Banach space | quasi-barrelled space | quasi-complete space | quasi-normed space | seminormed space | sequentially complete space | stereotype space | topological vector space | webbed space

A^1(D, dλ^2) | A^2(D, dλ^2) | ℬ(D, dλ^2) | L^∞(T;X) | a^1(D, dλ^2) | a^2(D, dλ^2) | ℬ^h(D, dλ^2) | h^2 | h^∞ | ℬ_0^h(D, dλ^2) | H^2 | H^∞ | L^2(D, dλ^2) | L^∞(D, dλ^2) | ℬ_0(D, dλ^2) | c_0(Z^+, dη) | ℓ^2(Z^+, dη) | ℓ^∞(Z^+, dη)

1920 to 1922

Stefan Banach (mathematician)

Hans Hahn | Eduard Helly

Gustave Choquet. Lectures on Analysis. Vol. I: Integration and Topological Vector Spaces. p. 25, 1969. Paul Garrett. "Banach and Fréchet Spaces of Functions." 2014. http://www.math.umn.edu/~garrett/m/fun/notes_2012-13/02_spaces_fcns.pdf. John Horvath. Topological Vector Spaces and Distributions. Vol. I. p. 9, 1966. Taqdir Husain. The Open Mapping and Closed Graph Theorems in Topological Vector Spaces. p. 16, 1965. Taqdir Husain and S.M. Khaleelulla. Barrelledness in Topological and Ordered Vector Spaces. p. 13, 1978. Gottfried Köthe. Topological Vector Spaces. I. p. 126, 1969. Lawrence Narici and Edward Beckenstein. Topological Vector Spaces, 2nd ed. p. 14, 2011. Alexander Provan Robertson and Wendy Robertson. Topological Vector Spaces. p. 60, 1964. Helmut H. Schaefer and Manfred P.H. Wolff. Topological Vector Spaces, 2nd ed. p. 41, 1999. François Trèves. Topological Vector Spaces, Distributions and Kernels. p. 97, 1967. Albert Wilansky. Modern Methods in Topological Vector Spaces. p. 27, 1978. Yau-Chuen Wong. Introductory Theory of Topological Vector Spaces. p. 18, 1992.