Resolvability of spaces having small spread or extent
| 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 | In a recent paper O. Pavlov proved the following two interesting resolvability results: (1) If a space $X$ satisfies $Δ(X) > \ps(X)$ then $X$ is maximally resolvable. (2) If a $T_3$-space $X$ satisfies $Δ(X) > \pe(X)$ then $X$ is $ω$-resolvable. Here $\ps(X)$ ($\pe(X)$) denotes the smallest successor cardinal such that $X$ has no discrete (closed discrete) subset of that size and $Δ(X)$ is the smallest cardinality of a non-empty open set in $X$. In this note we improve (1) by showing that $Δ(X) >$ $\ps(X)$ can be relaxed to $Δ(X) \ge$ $\ps(X)$. In particular, if $X$ is a space of countable spread with $Δ(X) > ω$ then $X$ is maximally resolvable. The question if an analogous improvement of (2) is valid remains open, but we present a proof of (2) that is simpler than Pavlov's. | |
| dc.identifier | https://arxiv.org/abs/math/0609091 | |
| dc.identifier | http://arxiv.org/abs/math/0609091 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116368 | |
| dc.subject | General Topology | |
| dc.subject | Logic | |
| dc.subject | 54A35 (Primary) 03E35, 54A25 (Secondary) | |
| dc.title | Resolvability of spaces having small spread or extent | |
| dc.type | text |