Timeline for When are the closed convex subsets countable intersections of halfspaces
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 9, 2020 at 23:08 | comment | added | Michael | On the positive side, the paper seems to be well written with a simple and easy flow, it just uses a lot of loaded terminology that is hard for me to plug into. I would have to read the paper in detail from start to finish, looking up on wikipedia every 5 minutes to get the different terminology, to be confident in applying the results even to basic spaces like $\mathbb{R}^n$. | |
| Jul 9, 2020 at 22:58 | comment | added | Michael | Note to functional analysis mathematicians: Please tell us if your results hold for $\mathbb{R}^n$. Anyway I can likely prove the $\mathbb{R}^n$ case myself but it would have been nice to have a reference, at least the case when a set is closed, bounded, and convex in $\mathbb{R}^n$ it seems easy-to-prove (the case of just closed and convex seems more tricky). | |
| Jul 9, 2020 at 22:55 | comment | added | Michael | I pulled up this paper but I could not discern a clear answer. Prop 3.3 seems the closest match and says that if some $B_{X^*}$ thingy satisfies a Corson compact thingy then "every closed convex subset in X is constructible if and only if there exists at least one closed bounded convex constructible set in X." I'm not sure what other (Banach space?) assumptions X is assumed to have. I don't even know if $\mathbb{R}^n$ satisfies the Corson-and-$B_{X^*}$ thingy. This paper could have been more helpful if the authors had written a few sentences to give down-to-earth interpretations. | |
| Sep 15, 2017 at 1:25 | vote | accept | LCO | ||
| Sep 15, 2017 at 1:07 | history | answered | Igor Rivin | CC BY-SA 3.0 |