Timeline for Agreement of two topologies on a linear space
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 2, 2013 at 6:28 | comment | added | Tom LaGatta | @NateEldredge, thanks for the tip of Bogachev's book, it's very relevant. In particular, here is a nice theorem which I had been looking for. Theorem 3.6.5. (p. 121) Let $\mu$ be a Radon measure on a Fréchet space $X$. There exists a linear subspace $E \subseteq X$ of full $\mu$-measure which is a reflexive, separable Banach space, and its unit ball is compact in the topology of $X$. | |
| Jul 2, 2013 at 6:22 | comment | added | Tom LaGatta | @NateEldredge, actually the abstract nonsense construction is what I was looking for, except that Jochen's counterexample below means that it won't agree with the subspace topology, so it doesn't really matter. | |
| Jul 2, 2013 at 6:09 | vote | accept | Tom LaGatta | ||
| Jun 26, 2013 at 7:34 | answer | added | Jochen Wengenroth | timeline score: 4 | |
| Jun 26, 2013 at 3:35 | comment | added | Nate Eldredge | You should be able to do some abstract nonsense construction with the axiom of choice to achieve 1 and probably 2. But I doubt this is what you want, so maybe you want to add some other conditions. By any chance is the discussion of "linear supports" in section 3.6 of Bogachev's Gaussian Measures relevant? | |
| Jun 26, 2013 at 0:00 | history | asked | Tom LaGatta | CC BY-SA 3.0 |