J Austral Math Soc Ser A 53 pp281--285, 1992.

On Pairwise Paracompactness

M. Ganster and I. L. Reilly

Abstract

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, t, s) to be d-pairwise paracompact if and only if every t open (s open) cover of X admits a tÚs open refinement which is tÚs locally finite. It is shown that pairwise paracompactness implies d-pairwise paracompactness, and that the converse is false.

1991 AMS Subject Classification: 54D18, 54E55

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Authors

M. Ganster

Institut für Mathematik, Technische Universität Graz, Graz, Austria.

I. L. Reilly

Department of Mathematics and Statistics, University of Auckland, Auckland, New Zealand.