Timeline for Showing that $C(X,Y)$ is separable when $X$ is compact Hausdorff but $Y$ is just a separable Frechet space
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 14, 2021 at 5:56 | comment | added | Wlod AA | Oh, there is also the Frechet assertion that $\ C(X\ Y)\ $ is Frechet. It is isometrically/linearly embedded in the inverse limit of a sequence of R^n spaces (each with the max norm), with Lip_1 projections. | |
| Jul 14, 2021 at 5:41 | comment | added | Wlod AA | Never mind Frechet. When $\ X\ $ is metric and compact, and $\ Y\ $ is metric and separable then $\ C(X\ Y)\ $ is separable. #### This is textbook knowledge, no need to ask MO. | |
| Jul 13, 2021 at 18:30 | vote | accept | Isaac | ||
| Jul 13, 2021 at 13:39 | answer | added | KP Hart | timeline score: 2 | |
| Jul 13, 2021 at 11:12 | comment | added | Jochen Wengenroth | The tensor product $C(X)\otimes Y$ is dense in $C(X,Y)$. | |
| Jul 13, 2021 at 8:30 | comment | added | Joel David Hamkins | Fréchet space: en.wikipedia.org/wiki/Fr%C3%A9chet_space | |
| Jul 13, 2021 at 7:30 | history | asked | Isaac | CC BY-SA 4.0 |