Timeline for A question about realcompact spaces
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2023 at 17:02 | vote | accept | Mehmet Onat | ||
| Jan 9, 2023 at 3:47 | history | edited | Taras Banakh | CC BY-SA 4.0 |
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| Jan 9, 2023 at 3:44 | comment | added | Taras Banakh | @Anonymous Yes, you are right, $X$ is not countably compact, and cannot be countably compact if $\beta X\setminus\upsilon X$. Thanks for the comment. I have removed the corresponding line from my answer. | |
| Jan 8, 2023 at 21:48 | comment | added | Anonymous | I must be missing something, but is it clear that $X$ is countably compact? The set $K$ can be assumed to be a cozero set of $\omega^*$. (That is what you get if each of the sets $U_n$ is closed as well as open and $f_n$ is the characteristic function of $U_n$.) But $K$ is contained in $\beta X \setminus X$, and a subset of $\omega$ whose accumulation points are in $K$ has no accumulation points in $X$. | |
| Jan 8, 2023 at 19:04 | history | edited | Taras Banakh | CC BY-SA 4.0 |
edited body
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| Jan 8, 2023 at 19:03 | comment | added | Taras Banakh | @Anonymous Yes! Thank you. Of course, it had to be $f_n^{-1}(1)$. | |
| Jan 8, 2023 at 13:58 | comment | added | Anonymous | Did you want $K_n$ to be $f_n^{-1}(1)$ rather than $f_n^{-1}(0)$? | |
| Jan 7, 2023 at 7:30 | history | edited | Taras Banakh | CC BY-SA 4.0 |
added 55 characters in body
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| Jan 7, 2023 at 5:43 | history | answered | Taras Banakh | CC BY-SA 4.0 |