Some covering properties of spaces
by
Ljubiša D.R. Kočinac
Faculty of Philosophy, University of Nis, 18000 Nis, Yugoslavia

Let \Cal A and \Cal B be collections of open covers of a space X and let \Cal K be a family of subsets of X. We consider some properties of X of the following two kinds:

(1) For every sequence (\Cal U_n: n Î N) of members of \Cal A there is a sequence (\Cal V_n:n Î N) such that for each n, \Cal V_n is a subfamily of \Cal U_n and È{\Cal V_n: n Î N} Î \CalB;

(2) For every sequence (\Cal U_n:n Î N) in \Cal A there is a sequence (\Cal V_n:n Î N) [resp. (K_n:n Î N)] such that for each n, \Cal V_n is a subfamily of \Cal U_n [resp. K_n is an element of \Cal K] and {St(È\Cal V_n, \Cal U_n):n Î N} Î \Cal B [resp. {St(F_n, \Cal U_n):n Î N} Î \Cal B].

Date received: June 15, 1998