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On the extent of star countable spaces
Authors:Ofelia T. Alas  Lucia R. Junqueira  Jan van Mill  Vladimir V. Tkachuk  Richard G. Wilson
Affiliation:1.Instituto de Matemática e Estatística,Universidade de S?o Paulo,S?o Paulo,Brasil;2.Department of Mathematics,VU University Amsterdam,Amsterdam,Netherlands;3.Departamento de Matematicas,Universidad Autónoma Metropolitana,Iztapalapa,Mexico, D.F.
Abstract: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.
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