Star covering properties and neighborhood assignments

Abstract

Following the idea of van Mill, Tkachuk, and Wilson (2007), we define a space X to be neighborhood assignment P (briefly NA-P, where P is a class of topological spaces) if for any neighbourhood assignment {O_x : x ∈ X} there is a subspace Y ⊂ X such that Y has the property P and ⋃_x∈Y O_x = X. In this paper we investigate the classes of NA-P spaces and compare them with the star covering properties for some class of topological spaces P.