Timeline for Compact open topology on $2^{\beta S}$ with $S$ a set
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2017 at 9:46 | vote | accept | Evgeny Kuznetsov | ||
| Mar 3, 2017 at 9:27 | answer | added | Uri Bader | timeline score: 5 | |
| Mar 3, 2017 at 7:19 | history | edited | Evgeny Kuznetsov | CC BY-SA 3.0 |
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| Mar 2, 2017 at 10:28 | history | edited | Evgeny Kuznetsov | CC BY-SA 3.0 |
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| Mar 2, 2017 at 10:21 | comment | added | Evgeny Kuznetsov | By use of Ascoli's theorem, thanks. | |
| Mar 2, 2017 at 9:57 | comment | added | Uri Bader | Fix a point $x$ in the boundary. For every point $y$ in $S$ consider all functions which are 0 on $x$ and $1$ on $y$. The intersection of this collection over all $y$ is empty. (in another way: the collection of all functions is not equicontinuous at $x$). | |
| Mar 2, 2017 at 9:52 | history | edited | Evgeny Kuznetsov | CC BY-SA 3.0 |
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| Mar 2, 2017 at 9:36 | comment | added | Evgeny Kuznetsov | Thanks, and how do you see that it is not a compact in case $S$ infinite? | |
| Mar 2, 2017 at 9:34 | comment | added | Uri Bader | I am sorry, it is not compact if $S$ is infinite. I got confused. I guess you should edit your question and explain what $2^{\beta S}$ means. | |
| Mar 2, 2017 at 9:25 | comment | added | Evgeny Kuznetsov | But how do you know that $2^{\beta S}$ is a compact? Is it clear and I do not know? Compactness is exactly I want to know about $2^{\beta S}$. I guess $2^{\beta S}$ is a compact iff $S$ is finite. | |
| Mar 2, 2017 at 9:23 | comment | added | Uri Bader | A continuous bijective map between Hausdorff compact spaces is a homeomorphism (because it is closed). | |
| Mar 2, 2017 at 9:21 | comment | added | Evgeny Kuznetsov | @Uri Bader I want $2^{\beta S}$ to be an exponent of $2$ by $\beta S$. Of course I consider the continuous maps. The restriction is bijection, but how do you see it is an homeomorphism? Thanks for a feedback | |
| Mar 2, 2017 at 9:11 | comment | added | Uri Bader | What do you mean by $2^{\beta S}$? all maps? only the continuous ones? if all maps, why will you expect any relation with the structure of $\beta S$? if only continuous, note that the restriction map to $2^S$ is a homeomorphism. | |
| Mar 2, 2017 at 6:46 | history | asked | Evgeny Kuznetsov | CC BY-SA 3.0 |