Timeline for Solidification of free abelian group on compact Hausdorff space
Current License: CC BY-SA 4.0
3 events
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| Feb 26, 2021 at 13:59 | comment | added | Jan Steinebrunner | Thank you for the quick and detailed answer. For completeness sake, let me add the following comment: Since $\mathcal{M}(S)$ is a Smith space it is isomorphic to its double dual $\mathcal{M}(S) = \underline{\mathrm{Hom}}_{\mathbb{R}}(\underline{\mathrm{Hom}}_{\mathbb{R}}(\mathcal{M}(S), \mathbb{R}), \mathbb{R})$ and moreover, by what you said, $\underline{\mathrm{Hom}}_{\mathbb{R}}(\mathcal{M}(S), \mathbb{R}) = \underline{\mathrm{Hom}}_{\mathbb{R}}(\mathbb{R}[S]^{\mathcal{M}-cpl}, \mathbb{R}) = C(S, \mathbb{R})$. This implies the expression $\mathcal{M}(S)$ that I mentioned in the question. | |
| Feb 25, 2021 at 19:55 | vote | accept | Jan Steinebrunner | ||
| Feb 25, 2021 at 19:44 | history | answered | Peter Scholze | CC BY-SA 4.0 |