J Austral Math Soc Ser A 48 pp235--245, 1990.

Pairwise Completion Regularity as a Separation Axiom

J. M. Aarts and M. Mrsevic

Abstract

Focussing on complete regularity, we discuss the separation properties of bitopical spaces. The unifying concept is that of separation by a pair of bases (B₁, B₂) for the closed sets of a bitopological space (S, J₁, J₂). For various separation properties a characterization is presented in terms of separation by a pair of closed bases. This is extended to results concerning pairs of subbases. Here the notion of screening by pairs of subbases plays a central role and the characterization of complete regularity in a natural way fits in between those of regularity and normality. In the key lemma the relation with quasi-proximities is exhibited.

1980 AMS Subject Classification (1985 Revision): primary 54E55; secondary 54D15

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Authors

J. M. Aarts

Delft University of Technology, Delft, The Netherlands.

M. Mrsevic

University of Belgrade, Belgrade, Yugoslavia.