Timeline for Is $\text{Sym}(\omega)/\text{(fin)}$ embeddable in $\text{Sym}(\omega)$?
Current License: CC BY-SA 4.0
9 events
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| Nov 27, 2023 at 10:08 | comment | added | Sean Eberhard | Maybe this answer should be posted on the original question too (maybe with an extra word or reference about why $\mathrm{Sym}(\omega)$ has the automatic continuity property?), since it is substantially different from the answer given there. | |
| Nov 27, 2023 at 7:18 | vote | accept | Dominic van der Zypen | ||
| Nov 27, 2023 at 6:33 | comment | added | YCor | @YemonChoi it's just the pointwise convergence topology (i.e., it is equal, and not just an analogue, to the topology induced by the product topology of the countable product $\omega^\omega$). | |
| Nov 26, 2023 at 20:13 | comment | added | Yemon Choi | Thanks @JoelDavidHamkins | |
| Nov 26, 2023 at 19:39 | comment | added | Joel David Hamkins | @YemonChoi There is a natural topology whose basic open sets are the permutations extending some finite partial map. This is an analogue of the product topology, and the finitely supported permutations are dense, since any finite injective map can be extended to a finitely supported permutation. | |
| Nov 26, 2023 at 19:08 | comment | added | Yemon Choi | Also, what is the topology on Sym($\omega$) with respect to which you claim that (fin) is dense in it? | |
| Nov 26, 2023 at 19:02 | comment | added | Yemon Choi | Surely you mean "is trivial" rather than "is the identity"? | |
| S Nov 26, 2023 at 16:58 | review | First answers | |||
| Nov 26, 2023 at 17:15 | |||||
| S Nov 26, 2023 at 16:58 | history | answered | Account will self-destruct | CC BY-SA 4.0 |