Timeline for Showing a filter with a certain property on the power set of $\mathbb{Z}$ is a one point filter
Current License: CC BY-SA 3.0
13 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Jul 19, 2015 at 14:31 | history | edited | Andrés E. Caicedo |
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| Jul 19, 2015 at 12:01 | history | edited | Dominic Michaelis | CC BY-SA 3.0 |
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| May 13, 2013 at 5:57 | vote | accept | Dominic Michaelis | ||
| May 9, 2013 at 23:22 | comment | added | Joseph Van Name | I edited my answer to also include the topological proof that every ultrafilter such that each function $f:P_{0}(X)\rightarrow X$ is constant almost everywhere. I however should mention that the topological proof is very similar to the purely combinatorial proof. | |
| May 8, 2013 at 12:20 | comment | added | Joseph Van Name | In other words, one needs to show that $\\{(f(A))_{f\in\mathcal{B}}|A\in P_{0}(X)\\}$ is a closed subspace of the product space $X^{\mathcal{B}}$. | |
| May 8, 2013 at 4:20 | comment | added | Joseph Van Name | I wonder if there is a topological proof of this result or of similar results. Let $\mathcal{B}$ be the set $\mathcal{A}$ unioned with the set of all functions $f:P_{0}(X)\rightarrow X$ with finite range. Give $X$ the discrete uniformity and give $P_{0}(X)$ the coarsest uniformity such that every $f\in\mathcal{B}$ is uniformly continuous. Then the completion of $P_{0}(X)$ is precisely the set of all ultrafilters $U$ on $P_{0}(X)$ such that every mapping $f\in\mathcal{A}$ is constant on some set in $U$. Thus, it suffices to show that $P_{0}(X)$ is a complete uniform space. | |
| May 8, 2013 at 4:17 | history | edited | Joseph Van Name |
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| May 6, 2013 at 20:16 | history | edited | Joseph Van Name |
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| May 6, 2013 at 20:02 | answer | added | Joseph Van Name | timeline score: 7 | |
| May 5, 2013 at 21:18 | history | edited | Dominic Michaelis | CC BY-SA 3.0 |
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| May 5, 2013 at 13:54 | history | asked | Dominic Michaelis | CC BY-SA 3.0 |