Timeline for Integral in a σ−convex set.
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 5, 2011 at 7:35 | vote | accept | TaQ | ||
| May 5, 2011 at 7:33 | comment | added | TaQ | That is a nice answer which I accept. The example obviously also works with $E=L^p([0,1])$ for $1\le p < +\infty$ . Saying that a set $U$ in a sequentially complete Hausdorff locally convex space $E$ is integral closed iff $\int_0^1\gamma\in U$ whenever $\gamma:[0,1]\to E$ is continuous with ${\rm rng\ }\gamma\subseteq U$ , we see that not even for separable Banach spaces does σ−convexity imply being integral closed. On the other hand, Hahn−Banach implies that (in sequentially complete LCS) open and closed convex sets are integral closed. | |
| May 4, 2011 at 19:34 | history | answered | Gerald Edgar | CC BY-SA 3.0 |