Timeline for Characterization of pretty compact spaces
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2021 at 10:05 | vote | accept | Norbert | ||
| Feb 5, 2021 at 21:29 | comment | added | Norbert | Now it is clear. Thank you! | |
| Feb 5, 2021 at 19:26 | history | edited | KP Hart | CC BY-SA 4.0 |
added 283 characters in body
|
| Feb 5, 2021 at 19:23 | comment | added | KP Hart | No, I added further explanation above. | |
| Feb 5, 2021 at 18:56 | comment | added | Norbert | Problem 3.12.24(c) in Engelking's General Topology states that the Cartesian product $X$ of compact Hausdorff spaces $\{X_s:s\in S\}$ is the Stone-Cech compactification of their $\Sigma$ product. By 2.7.14 from the same book the $\Sigma$ product of the family $\{X_s:s\in S\}$ is a set of the form $$\{x\in X: \operatorname{Card}(\{s\in S: x_s\neq a_s\})\leq \aleph_0 \}$$ for some $a\in X$. Clearly $\Sigma$ products are quite different from $X\setminus \{a\}$. So I don't think uncountable products of compact Hausdorff spaces are pretty compact. Am I right? | |
| Feb 5, 2021 at 12:56 | history | answered | KP Hart | CC BY-SA 4.0 |