First countable spaces without point-countable $π$-base
| dc.creator | Juhasz, Istvan | |
| dc.creator | Soukup, Lajos | |
| dc.creator | Szentmiklossy, Zoltan | |
| dc.date | 2007-03-25 | |
| dc.date.accessioned | 2026-07-07T07:53:52Z | |
| dc.date.available | 2026-07-07T07:53:52Z | |
| dc.description | We answer several questions of V. Tkačuk from [Point-countable $π$-bases in first countable and similar spaces, Fund. Math. 186 (2005), pp. 55--69.] by showing that (1) there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable $π$-base (in fact, the order of any $π$-base of the space is at least $\aleph_ω$); (2) if there is a $κ$-Suslin line then there is a first countable GO space of cardinality $κ^+$ in which the order of any $π$-base is at least $κ$; (3) it is consistent to have a first countable, hereditarily Lindel\" of regular space having uncountable $π$-weight and $ω_1$ as a caliber (of course, such a space cannot have a point-countable $π$-base). | |
| dc.identifier | https://arxiv.org/abs/math/0703728 | |
| dc.identifier | http://arxiv.org/abs/math/0703728 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126390 | |
| dc.subject | General Topology | |
| dc.subject | 54A25 (Primary), 54A35, 54D20, 54D70, 54F05 (Secondary) | |
| dc.title | First countable spaces without point-countable $π$-base | |
| dc.type | text |