Timeline for Separation-free topological completeness notion
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 2, 2017 at 22:05 | comment | added | Włodzimierz Holsztyński | ("hmmm?" -- nothing special; a confession like "Cannot really claim that I have immediate urgent motivation" is rare in mathematical writings). | |
| May 2, 2017 at 4:22 | comment | added | მამუკა ჯიბლაძე | @WłodzimierzHolsztyński -- hmmm? | |
| May 2, 2017 at 1:01 | comment | added | Włodzimierz Holsztyński | "Cannot really claim that I have immediate urgent motivation to study this question" -- hmmmm... | |
| May 2, 2017 at 0:36 | history | edited | Todd Trimble |
completeness tag removed per meta discussion
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| Apr 18, 2016 at 21:22 | comment | added | Taras Banakh | (1) Writing that $\mathcal F$ tends to $\bigcap\mathcal F$ I had in mind that for every neighborhood $U$ of $\bigcap \mathcal F$ some set $F\in\mathcal F$ is contained in $U$; (2) Such spaces should be quite exotic, in particular, not $T_1$; (3) You asked about Cech-complete spaces-- they are countable intersections of open subsets in compact spaces. That is why countable family is natural in this context. | |
| Apr 18, 2016 at 5:09 | comment | added | მამუკა ჯიბლაძე | @TarasBanakh Looks very attractive! Three questions: (1) could you say more precisely what do you mean by "tends in the natural sense"? (2) what about spaces with $({\mathcal U}_n)_n$ as above such that for no filter $\mathcal F$ of closed sets is some $F\in\mathcal F$ is contained in some set of ${\mathcal U}_n$ for every $n$? (3) the fact that the system of covers is countable looks somehow arbitrary, what happens if one asks for any system of covers, not necessarily countable? For example, the collection of all open covers? Or the single cover consisting of all opens? | |
| Apr 17, 2016 at 22:06 | comment | added | Taras Banakh | It seems that the Cech completeness can be defined without separation axioms: a topological space $X$ is Cech complete if there exists a sequence $(\mathcal U_n)_{n\in\omega}$ of open covers of $X$ such that for any filter $\mathcal F$ of closed subsets such that for every $n$ some set $F\in\mathcal F$ is contained in some set of $\mathcal U_n$ the intersection $\bigcap \mathcal F$ is compact and $\mathcal F$ tends to this intersection (in the natural sense). Is this good reformulations? | |
| Apr 17, 2016 at 15:05 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 3.0 |
typo
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| Apr 17, 2016 at 14:46 | history | asked | მამუკა ჯიბლაძე | CC BY-SA 3.0 |