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Martin Sleziak
Martin Sleziak
6:17 AM
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
2:56 PM
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
3:56 PM
Looking at the question, perhaps 4-manifolds might be a suitable tag. (Probably better than euler-characteristics.)
 
Martin Sleziak
Martin Sleziak
4:10 PM
Would perhaps gt.geometric-topology be a good top-level tag for this question?
 

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