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A generalization of Tong's theorem and properties of pairwise perfectly normal spaces
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 39 / Issue 3 / December 1985
- Published online by Cambridge University Press:
- 09 April 2009, pp. 353-359
- Print publication:
- December 1985
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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)–closed set is the zero of a P(Q)–l.s.c. and Q(P)–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.
binary relations.