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Pairwise complete regularity as a separation axiom

Part of: Spaces with richer structures Fairly general properties

Published online by Cambridge University Press:  09 April 2009

J. M. Aarts  and
M. Mršević
J. M. Aarts
Affiliation:
Delft University of Technology DelftThe Netherlands
M. Mršević
Affiliation:
University of BelgradeBelgrade, Yugoslavia
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Abstract

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Focussing on complete regularity, we discuss the separation properties of bitopological 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.

Keywords

(sub)base for the closed setsseparation axiomscomplete regularity.

MSC classification

Secondary: 54E55: Bitopologies 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 2 , April 1990 , pp. 235 - 245
Copyright
Copyright © Australian Mathematical Society 1990

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