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On pairwise paracompactness

Part of: Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

M. Ganster  and
I. L. Reilly
M. Ganster
Affiliation:
Institut für MathematikTechnische Universität GrazGraz, Austria
I. L. Reilly
Affiliation:
Department of Mathematics and StatisticsUniversity of AucklandAuckland New, Zealand
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Abstract

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This paper answers a recent question concerning the relationship between two notions of paracompactness for bitopological spaces. Romaguera and Marin defined pairwise paracompactness in terms of pair open covers, motivated by a characterization of paracompactness due to Junnila. On the other hand, Raghavan and Reilly defined a bitopological space (X, τ, σ) to be δ-pairwise paracompact if and only if every τ open (σ open) cover of X admits a τ V σ open refinement which is τ V σ locally finite. It is shown that pairwise paracompactness implies δ-pairwise paracompactness, and that the converse is false.

Keywords

bitopological spacepairwise paracompactpairwise regular.

MSC classification

Secondary: 54E55: Bitopologies
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 2 , October 1992 , pp. 281 - 285
Copyright
Copyright © Australian Mathematical Society 1992

References

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