Monday, March 2, 2015

all Banach spaces are (Hausdorff)locally convex spaces

Locally convex topological vector space - Wikipedia, the free ...

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A locally convex space is Hausdorff if and only if it has a separated family of seminorms. Many authors take the Hausdorff criterion in the definition.
  • Locally convex space which is not Banach. - Mathematics ...

    math.stackexchange.com/.../locally-convex-space-which-is... 翻譯這個網頁
    2013年2月1日 - I know that all Banach spaces are (Hausdorff)locally convex spaces. I would like to verify that the converse is not true by giving an example of a ...
  • [PDF]Locally Convex Vector Spaces I: Basic Local Theory

    www.math.ksu.edu/~nagy/func-an-2007.../lcvs-1.pdf 翻譯這個網頁
    A locally convex topological vector space is a locally convex vector space, whose topology is Hausdorff. Since convexity is translation invariant, for a linear ...
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