Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-13T07:32:05.081Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Bing, R. H., ‘Metrization of topological spaces’, Canad. J. Math. 3 (1951), 175–186.CrossRefGoogle Scholar
[2]Girhiny, J., ‘Preservation of topological properties under lattice operations and relations’, McMaster Mathematical Report 33 (1970).Google Scholar
[3]Junnila, H. J. K., Covering properties and quasi-uniformities of topological spaces, Thesis, Virginia Polytechnic Institute and State University (1978).Google Scholar
[4]Kowalsky, H. J., Topological Spaces (Academic Press, New York, 1965).Google Scholar
[5]Raghavan, T. G. and Reilly, I. L., ‘A new bitopological paracompactness’, J. Austral. Math. Soc. (Series A) 41 (1986), 268–274.CrossRefGoogle Scholar
[6]Romaguera, S. and Marin, J., ‘On the bitopologial extension of the Bing metrization theorem’, J. Austral. Math. Soc. (Series A) 44 (1988), 233–241.Google Scholar