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Results tagged with locally-convex-spaces
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user 454
Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.
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)
…
- 41.1k
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: …
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