Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy
Published 2013-11-07Version 1
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.
New bounds on the cardinality of Hausdorff spaces and regular spaces
The double density spectrum of a topological space
A bound for the density of any Hausdorff space
![QR code for arXiv:1311.1719 [math.GN]](http://oss.arxitics.com/images/favicon.svg)