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

Part of: Basic constructions Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

Manuel López-Pellicer  and
Angel Gutiérrez
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.

Keywords

binary relationpairwise perfectly normalperfect functionsproductquotientsemicontinuous functionsubspacesum

MSC classification

Secondary: 54E55: Bitopologies 54B10: Product spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 3 , December 1985 , pp. 353 - 359
Copyright
Copyright © Australian Mathematical Society 1985

References

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