Timeline for countable topological spaces of uncountable weight
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 27, 2014 at 23:39 | history | edited | user9072 |
edited tags
|
|
| Oct 14, 2012 at 17:56 | answer | added | Henno Brandsma | timeline score: 4 | |
| Aug 22, 2012 at 23:34 | comment | added | Andreas Blass | The Appert space, pointed out in Ramiro de la Vega's answer, also fits the description in my previous comment. | |
| Aug 22, 2012 at 19:12 | answer | added | Ramiro de la Vega | timeline score: 7 | |
| Aug 21, 2012 at 15:34 | comment | added | Andreas Blass |
In the hope of avoiding an explosion of variants of Stefan's proof, I note that his and Arthur's proofs are both special cases of the following (and there are lots more special cases). Take a countable set $S$ and a filter $F$ on S having no countable base and containing all cofinite subsets of $S$. Topologize $S\cup\{p\}$ (where $p\notin S$) by making a subset $U$ open if either $p\notin U$ or $(U\cap S)\in F$. Then $X$ is normal because of any two disjoint (closed) sets one is open. There is no countable base for the topology because there is no countable neighborhood base at $p$.
|
|
| Aug 21, 2012 at 5:17 | answer | added | user642796 | timeline score: 5 | |
| Aug 20, 2012 at 22:20 | answer | added | Stefan Geschke | timeline score: 5 | |
| Aug 20, 2012 at 21:52 | history | edited | Ramsey | CC BY-SA 3.0 |
edited title
|
| Aug 20, 2012 at 21:09 | history | asked | Pedro Perez | CC BY-SA 3.0 |