Regular spaces of small extent are omega-resolvable
General Topology
2013-11-08 v1
Abstract
We improve some results of Pavlov and of Filatova, respectively, concerning a problem of Malychin by showing that every regular space X that satisfies Delta(X)>ext(X) is omega-resolvable. Here Delta(X), the dispersion character of X, is the smallest size of a non-empty open set in X and ext(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindel\"of spaces of uncountable dispersion character are omega-resolvable. We also prove that any regular Lindel\"of space X with |X|=\Delta(X)=omega_1 is even omega_1-resolvable. The question if regular Lindel\"of spaces of uncountable dispersion character are maximally resolvable remains wide open.
Keywords
Cite
@article{arxiv.1311.1719,
title = {Regular spaces of small extent are omega-resolvable},
author = {Istvan Juhasz and Lajos Soukup and Zoltan Szentmiklossy},
journal= {arXiv preprint arXiv:1311.1719},
year = {2013}
}