A note on the comparison of topologies

A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We...

Full description

Saved in:
Bibliographic Details
Published in:International journal of mathematics and mathematical sciences 2001-01, Vol.26 (4), p.233-237
Main Author: Kovar, Martin M
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiom S2 which is appropriate for the study of the bitopological collapse. We also show that the property that may cause the collapse is much weaker than some modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I. L. Reilly (1977) regarding the comparison of topologies.
ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171201005518