Timeline for Compactness of $C(X,X)$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Mar 10, 2020 at 12:23 | vote | accept | Sh.M1972 | ||
| Mar 10, 2020 at 9:52 | comment | added | Sh.M1972 | @YCor, Indeed I only need the case when $X=A^G$ the shift space over finite alphabet $A$ and a f.g group $G$. The set of all cellular automata is a closed subset in this case but I want to see if it is compact or not. | |
| Mar 10, 2020 at 8:32 | history | edited | YCor |
edited tags
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| Mar 10, 2020 at 8:31 | comment | added | YCor | @M.Shahryari it's quite trivial to find $X$ with $C(X,X)$ not compact, so maybe you should reformulate the question taking this into account (e.g., asking about a characterization of $X$ such that $C(X,X)$ is compact). Note that (for $X$ compact) this is equivalent to asking when $C(X,X)$ is closed in $X^X$, and hence a related question is this one. | |
| Mar 10, 2020 at 8:19 | comment | added | Sh.M1972 | 2YCor yes thank you. | |
| Mar 10, 2020 at 8:18 | history | edited | Sh.M1972 | CC BY-SA 4.0 |
I deleted a sentence which was obvious by the compactness.
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| Mar 10, 2020 at 7:27 | comment | added | YCor | Note that a compact metric space is always complete and separable. | |
| Mar 10, 2020 at 7:06 | answer | added | Alexander Schmeding | timeline score: 2 | |
| Mar 10, 2020 at 6:55 | review | Close votes | |||
| Mar 17, 2020 at 3:05 | |||||
| Mar 10, 2020 at 6:40 | comment | added | abx | See the Arzelà–Ascoli theorem. | |
| Mar 10, 2020 at 6:16 | comment | added | Sh.M1972 | @erz Thank you so much. | |
| Mar 10, 2020 at 6:10 | comment | added | erz | For $X=[0,1]$ it will be non-compact. | |
| Mar 10, 2020 at 5:51 | history | asked | Sh.M1972 | CC BY-SA 4.0 |