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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.

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