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Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.

3 votes

When is a locally convex topological vector space normal or paracompact?

A paper dealing with this (and other) questions for the weak topology of a Banach space ... H. H. Corson, "The weak topology of a Banach space" Trans. Amer. Math. Soc. 101 (1961) 1--15. In that case: …
Gerald Edgar's user avatar
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7 votes

Closed convex hull in infinite dimensions vs. continuous convex combinations

No. Even in one dimension. Say $K$ is the open interval $(0,1)$. Show $0 \notin K^*$. Let $\mu$ be a probability measure with support contained in $(0,1)$. Indeed, $$ r(\mu) := \int_K x\,d\mu(x) …
Gerald Edgar's user avatar
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