Timeline for Extending open maps to Stone-Cech compactifications
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2011 at 15:55 | comment | added | Bill Johnson | Sure, post it on math.SE, Asaf. I don't have an account there. | |
| Oct 12, 2011 at 10:42 | comment | added | Asaf Karagila♦ | Bill: If you have a math.SE, could you post this on the linked question as well? If not, may I have your permission to post it as community wiki? | |
| Oct 12, 2011 at 10:41 | vote | accept | Asaf Karagila♦ | ||
| Oct 12, 2011 at 10:27 | comment | added | Emil Jeřábek | @Asaf: The indicator function of $2B$ is continuous, and its extension to $\beta X$ gives a partition of $\beta X$ into two clopen subsets that are easily seen to be the closures of $2B$ and its complement, respectively. (In general, if $C$ is a clopen subset of $W$, then the closure of $C$ in $\beta W$ is clopen.) By a similar argument, the closure of $\frac12Y$ omits all points $-1/(2n+1)$, hence it does not contain any neighbourhood of its element $0$. | |
| Oct 12, 2011 at 9:23 | comment | added | Asaf Karagila♦ | Bill, the extension is onto $\beta Y$, I also fail to see why the closure of $2B$ is clopen, and why the closure of $\frac{1}{2}Y$ is not clopen in $\beta Y$. | |
| Oct 11, 2011 at 23:33 | history | edited | Bill Johnson | CC BY-SA 3.0 |
Corrected typo
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| Oct 11, 2011 at 23:22 | history | answered | Bill Johnson | CC BY-SA 3.0 |