A generalization of Tong's theorem and properties of pairwise perfectly normal spaces

摘要

In this paper we give some properties of the pairwise perfectly normal spaces defined by Lane. In particular we prove that a space (X, P, Q) is pairwise perfectly normal if and only if every P(Q)a€“closed set is the zero of a P(Q)a€“l.s.c. and Q(P)a€“u.s.c. function. Also we characterize the pairwise perfect normality in terms of sequences of semicontinuous functions by means of a result which contains the known Tong's characterization of perfectly normal topological spaces, whose proof we modify by using the technique of binary relations.