Timeline for Convex hulls of compact sets
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 18, 2019 at 2:48 | comment | added | Robert Furber | In any locally convex space $E$, the closed convex hull of a precompact set $X$ is precompact (see Schaefer's Top. Vect. Sp., Chapter II, Section 4.3). It follows that if $E$ is quasi-complete (every closed bounded set is complete - automatically true if $E$ is complete), then the closed convex hull of $X$ is compact, being precompact and complete. | |
| Feb 9, 2014 at 17:47 | comment | added | Paul Fabel | mathoverflow.net/questions/6627/convex-hull-in-cat0 this related question is purportedly open | |
| Feb 1, 2014 at 0:52 | comment | added | Tom LaGatta | (note: that theorem requires that $H$ be locally convex and completely metrizable, which is satisfied for a Hilbert space $H$. The assumption of separability is not necessary) | |
| Jan 31, 2014 at 22:42 | comment | added | Tom LaGatta | Via Theorem 5.35 on that page, the answer is "yes" if one replaces "convex hull" with "closed convex hull". | |
| Jan 31, 2014 at 20:25 | review | Close votes | |||
| Feb 1, 2014 at 10:22 | |||||
| Jan 31, 2014 at 19:55 | review | Low quality posts | |||
| Jan 31, 2014 at 20:05 | |||||
| Jan 31, 2014 at 19:45 | comment | added | Francois Ziegler | Not necessarily. Proof by google, counterexample here. | |
| Jan 31, 2014 at 19:38 | history | asked | Tom LaGatta | CC BY-SA 3.0 |