Nagata's conjecture and countably compactifications in generic extensions
| dc.creator | Soukup, Lajos | |
| dc.date | 2006-10-13 | |
| dc.date.accessioned | 2026-07-07T07:29:03Z | |
| dc.date.available | 2026-07-07T07:29:03Z | |
| dc.description | Nagata conjectured that every $M$-space is homeomorphic to a closed subspace of the product of a countably compact space and a metric space. This conjecture was refuted by Burke and van Douwen, and A. Kato, independently. However, we can show that there is a c.c.c. poset $P$ of size $2^ω$ such that in $V^P$ Nagata's conjecture holds for each first countable regular space from the ground model (i.e. if a first countable regular space $X\in V$ is an $M$-space in $V^P$ then it is homeomorphic to a closed subspace of the product of a countably compact space and a metric space in $V^P$). In fact, we show that every first countable regular space from the ground model has a first countable countably compact extension in $V^P$, and then apply some results of Morita. As a corollary, we obtain that every first countable regular space from the ground model has a maximal first countable extension in model $V^P$. | |
| dc.identifier | https://arxiv.org/abs/math/0610432 | |
| dc.identifier | http://arxiv.org/abs/math/0610432 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117959 | |
| dc.subject | General Topology | |
| dc.subject | Logic | |
| dc.subject | 54D35, 54E18, 54A35, 03E3 | |
| dc.title | Nagata's conjecture and countably compactifications in generic extensions | |
| dc.type | text |