Timeline for Importance of separability vs. second-countability
Current License: CC BY-SA 3.0
8 events
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| Jun 5, 2013 at 20:24 | comment | added | The User | It is a very nice and interesting answer, but I accepted Ramiro’s answer, because it describes more that kind of property I was looking for. Thanks. | |
| May 20, 2013 at 21:40 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
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| May 19, 2013 at 19:31 | comment | added | Joseph Van Name | Yes. I did mean the size of an ultrapower. | |
| May 19, 2013 at 19:10 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
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| May 19, 2013 at 18:45 | comment | added | Andreas Blass | I'd go a bit further than "there are very similar proofs ... using independent sets and independent partitions." I think of the existence of continuum many independent partitions of $\mathbb N$ and the separability of a product of continuum many separable spaces as being essentially the same theorem. Each is deducible easily from the other. Being more combinatorial than topological, I tend to view the former (and its generalizations to higher cardinals) as the main point, and to view separability as a nice way to make it look topological for those whose tastes differ from mine. | |
| May 19, 2013 at 18:40 | comment | added | Andreas Blass | Concerning "the Rudin-Keisler ordering measures the size of an ultrafilter": Did you mean "the size of an ultrapower"? | |
| May 19, 2013 at 18:20 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
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| May 19, 2013 at 5:59 | history | answered | Joseph Van Name | CC BY-SA 3.0 |