A closed set and compact set in topological vector space

Asked Jul 21 '20 at 02:16

Active Jul 21 '20 at 02:16

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I have read the post in the link: A and B disjoint, A compact, and B closed implies there is positive distance between both sets

I wonder that the property in the link above is still correct in topological vector space or not? It means: If $A$ is closed, B is compact and $A\cap B = \varnothing$ then exist $V$ is neighborhood of $\theta$ that $$(A+V)\cap(B+V)=\varnothing$$

asked Jul 21 '20 at 02:16

Xiuwei Lee

See Theorem 1.10 in Rudin's FA. – Kavi Rama Murthy Jul 21 '20 at 05:24
@KaviRamaMurthy Thank you a lot. I have found the answer in the book you mention. – Xiuwei Lee Jul 21 '20 at 05:45

A closed set and compact set in topological vector space

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