For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω 1-monolithic compact space X, if C p(X)is star countable then it is Lindelöf.
@article{bwmeta1.element.doi-10_2478_s11533-011-0018-y,
author = {Ofelia Alas and Lucia Junqueira and Jan Mill and Vladimir Tkachuk and Richard Wilson},
title = {On the extent of star countable spaces},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {603-615},
zbl = {1246.54017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0018-y}
}
Ofelia Alas; Lucia Junqueira; Jan Mill; Vladimir Tkachuk; Richard Wilson. On the extent of star countable spaces. Open Mathematics, Tome 9 (2011) pp. 603-615. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0018-y/
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