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Fréchet Space

Description

A Fréchet space is a vector space that is locally convex and that is complete with respect to a translation-invariant metric. Also, a locally convex F-space.

Relationship graph

Relationship graph

More general classifications

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

Examples

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)

History

Maurice Fréchet (mathematician)

Timeline

Timeline

References

Gustave Choquet. Lectures on Analysis. Vol. I: Integration and Topological Vector Spaces. p. 353, 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. 136, 1966. Taqdir Husain. The Open Mapping and Closed Graph Theorems in Topological Vector Spaces. p. 19, 1965. Lawrence Narici and Edward Beckenstein. Topological Vector Spaces, 2nd ed. p. 93, 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. 49, 1999. Albert Wilansky. Modern Methods in Topological Vector Spaces. pp. 56 and 135, 1978. Yau-Chuen Wong. Introductory Theory of Topological Vector Spaces. p. 121, 1992.

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