Resolvability and monotone normality
| dc.creator | Juhasz, Istvan | |
| dc.creator | Soukup, Lajos | |
| dc.creator | Szentmiklossy, Zoltan | |
| dc.date | 2006-09-04 | |
| dc.date.accessioned | 2026-07-07T07:24:28Z | |
| dc.date.available | 2026-07-07T07:24:28Z | |
| dc.description | A space $X$ is said to be $κ$-resolvable (resp. almost $κ$-resolvable) if it contains $κ$ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). $X$ is maximally resolvable iff it is $Δ(X)$-resolvable, where $Δ(X) = \min\{|G| : G \ne \emptyset {open}\}.$ We show that every crowded monotonically normal (in short: MN) space is $ω$-resolvable and almost $μ$-resolvable, where $μ= \min\{2^ω, ω_2 \}$. On the other hand, if $κ$ is a measurable cardinal then there is a MN space $X$ with $Δ(X) = κ$ such that no subspace of $X$ is $ω_1$-resolvable. Any MN space of cardinality $< \aleph_ω$ is maximally resolvable. But from a supercompact cardinal we obtain the consistency of the existence of a MN space $X$ with $|X| = Δ(X) = \aleph_ω$ such that no subspace of $X$ is $ω_2$-resolvable. | |
| dc.identifier | https://arxiv.org/abs/math/0609092 | |
| dc.identifier | http://arxiv.org/abs/math/0609092 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116369 | |
| dc.subject | General Topology | |
| dc.subject | Logic | |
| dc.subject | 54A35 (Primary) 03E35, 54A25 (Secondary) | |
| dc.title | Resolvability and monotone normality | |
| dc.type | text |