Timeline for Convergent filters generated by (not necessarily countable) chains
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 3, 2023 at 5:32 | comment | added | PatrickR | @JosephVanName Should a $\kappa$-well based space be defined by $\mathscr{O}_{x}$ having a cofinal chain of cofinality at most $\kappa$ (instead of exactly $\kappa$)? | |
| Oct 16, 2023 at 13:15 | comment | added | Joseph Van Name | @PatrickR I overlooked the case when the two sides have different cofinalities, but now I corrected this. | |
| Oct 16, 2023 at 13:13 | history | edited | Joseph Van Name | CC BY-SA 4.0 |
added 175 characters in body
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| Oct 16, 2023 at 6:06 | comment | added | PatrickR | @JosephVanName You mentioned that totally ordered sets with the order topology are well-based. Is that really true? For example if we have a point and on the left of it we have a copy of $\omega_1$ and on the right of it a copy of $\omega$ reversed, then due to the different cofinalities on both sides, the point cannot have a local base of nbhds in a chain. (similar to showing that the partially ordered set $\omega_1\times\omega$ does not have a cofinal chain) | |
| Oct 16, 2023 at 5:19 | comment | added | PatrickR | Well-based spaces have also been called CLB (chain local base) in N. Howes, A note on transfinite sequences (1980). They were also mentioned, though not under these names, already by H. Herrlich (1967) when he defined (pseudo)radial spaces. | |
| Jul 15, 2015 at 22:15 | vote | accept | Rafał Gruszczyński | ||
| Apr 9, 2015 at 21:57 | comment | added | Rafał Gruszczyński | Joseph, thanks a lot for your effort. I have to digest it now and then I will probably have some more questions. But basically this has already helped me partially solved a problem which motivated the question. | |
| Apr 9, 2015 at 2:20 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
added 4027 characters in body
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| Apr 8, 2015 at 2:51 | history | answered | Joseph Van Name | CC BY-SA 3.0 |