Timeline for Stone–Čech compactification and an ultrafilter of regular closed sets
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 11, 2023 at 18:47 | history | edited | LSpice | CC BY-SA 4.0 |
Oops, missed one
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| Aug 11, 2023 at 12:03 | vote | accept | Mehmet Onat | ||
| Aug 10, 2023 at 20:48 | comment | added | Gro-Tsen | I thinks this other question and its references and answer are highly relevant to the present one. | |
| Aug 10, 2023 at 19:42 | comment | added | LSpice |
TeX note: \left and \righting all pairs of parentheses is harmless in terms of sizing if the contents are small enough (though it can be really weird looking when the contents are asymmetric about the midline: $\displaystyle\left(\sum_n n^{-s}\right)$), but it does weird things to the spacing. Compare $\mathcal R(X)$ \mathcal R(X) vs. $\mathcal R\left(X\right)$ \mathcal R\left(X\right).
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| Aug 10, 2023 at 19:41 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading and links to articles
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| Aug 10, 2023 at 17:57 | answer | added | KP Hart | timeline score: 3 | |
| Aug 7, 2023 at 8:00 | comment | added | მამუკა ჯიბლაძე | For the second, if this condition is satisfied, then $\gamma\beta X\approx\beta X$, so you can just define $\beta X\approx\gamma\beta X\to\gamma\beta Y\to\beta Y$, using that both $\beta$ and $\gamma$ are functorial. | |
| Aug 7, 2023 at 7:50 | comment | added | მამუკა ჯიბლაძე | For the first question the answer is no. If $\beta X$ is compact Hausdorff, the Stone space of ultrafilters of $\mathscr R(X)$ is the Gleason cover $\gamma\beta X$ of $\beta X$, and the limit map $\gamma\beta X\to\beta X$ is bijective iff $\beta X$ is extremally disconnected. | |
| Aug 7, 2023 at 6:17 | history | asked | Mehmet Onat | CC BY-SA 4.0 |