We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable. We also prove that any regular Lindelöf space X with |X| = Δ(X) = ω₁ is even ω₁-resolvable. The question whether regular Lindelöf spaces of uncountable dispersion character are maximally resolvable remains wide open.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-3,
author = {Istv\'an Juh\'asz and Lajos Soukup and Zolt\'an Szentmikl\'ossy},
title = {Regular spaces of small extent are $\omega$-resolvable},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {27-46},
zbl = {1315.54005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-3}
}
István Juhász; Lajos Soukup; Zoltán Szentmiklóssy. Regular spaces of small extent are ω-resolvable. Fundamenta Mathematicae, Tome 228 (2015) pp. 27-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-3/