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A new bitopological paracompactness

Part of: Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

T. G. Raghavan  and
I. L. Reilly
T. G. Raghavan
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand
I. L. Reilly
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand
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Abstract

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In this paper we define generalization of paracompactness for bitopological spaces. (X, τ1, τ2) is Δ-pairwise paracompact if and only if every τi open cover admits a τ1 ∨ τ2 open refinement which is τ1 ∨ τ2 locally finite. Every quasimetric space (X, τp, τq) is Δ-pairwise paracompact. An analogue of Michael's characterization of regular paracompact spaces is proved for Δ-pairwise paracompact spaces.

MSC classification

Secondary: 54E55: Bitopologies
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 2 , October 1986 , pp. 268 - 274
Copyright
Copyright © Australian Mathematical Society 1986

References

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