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Martin Sleziak
Martin Sleziak
06:17
New tags: krein-milman-theorem and extreme-points.
12
Q: Extreme points of convex compact sets

Fedor PetrovPreparing to a lecture on Krein--Milman theorem I read in W. Rudin's Functional analysis textbook (1973) that it is unknown whether any convex compact set in any topological vector space has an extreme point. Is it still unknown?

reference-request fa.functional-analysis convexity extreme-points krein-milman-theorem
 
9 hours later…
Martin Sleziak
Martin Sleziak
14:56
specific-question This question is currently in HNQ: Is there a closed non-smoothable 4-manifold with zero Euler characteristic? It has no top-level tag. (And probably also the euler-characteristics tag is a good fit and should be added. But I've mentioned the question here mainly because I am not sure which top-level tag would be suitable.)
5
Q: Is there a closed non-smoothable 4-manifold with zero Euler characteristic?

CihanI will just repeat the title: Is there a closed non-smoothable 4-manifold with zero Euler characteristic? I am guessing yes simply based on other existence theorems I have seen for 4-manifolds.

smooth-manifolds manifolds topological-manifolds
Martin Sleziak
Martin Sleziak
15:56
Looking at the question, perhaps 4-manifolds might be a suitable tag. (Probably better than euler-characteristics.)
Martin Sleziak
Martin Sleziak
16:10
Would perhaps gt.geometric-topology be a good top-level tag for this question?

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