Timeline for Are representations in computable analysis the equivalent to countably-generated condensed sets?
Current License: CC BY-SA 4.0
5 events
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| Aug 27, 2021 at 16:10 | history | edited | Arno | CC BY-SA 4.0 |
added references for a claim
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| Aug 24, 2021 at 1:58 | comment | added | Jason Rute | For (2), I totally agree that this is the question to answer. I now realize it is easy to faithfully embed represented spaces into the category of condensed sets using the functor taking $(X, \rho_X)$ to the class of functions $\rho_X \circ g : S \to X$ for continuous maps $g: S \to \text{dom}(\rho_X)$ and profinite $S$ (of any cardinality). One remaining question is, for which representative spaces $(X, \rho_X)$ is this functor full? I've verified it for any space for which $\text{dom}(\rho_X)$ is (locally?) compact, but it should be much larger! | |
| Aug 24, 2021 at 1:46 | comment | added | Jason Rute | For (3), note I made a mistake describing the endomorphisms of $\mathbb{R}/\mathbb{Q}$. I've now both verified that $\mathbb{R}/\mathbb{Q}$ has the same endomorphisms as a represented space as it does as a condensed set, and that the situation is as you describe: It's only obvious that $\mathbb{R}/\mathbb{Q} \to \mathbb{R}/\mathbb{Q}$ have endomorphisms corresponding to continuous multifunctions. | |
| Aug 23, 2021 at 13:23 | history | edited | Arno | CC BY-SA 4.0 |
added 12 characters in body
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| Aug 23, 2021 at 12:17 | history | answered | Arno | CC BY-SA 4.0 |