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

Published online by Cambridge University Press:  09 April 2009

Manuel López-Pellicer
Affiliation:
C´tedra de Matem´ticas, E.T.S.I. Agrónomos, Universidad Politécnica, Camino de Vera s.n., 46022-Valencia, Spain
Angel Gutiérrez
Affiliation:
Departamento de Matem´ticas, E.U. del Profesorado de E.G.B., Alcalde Reig, 8 46006-Valencia, Spain
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

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