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Publication detail
KOVÁR, M.
Original Title
A note on the comparison of topologies
Type
journal article - other
Language
English
Original Abstract
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 $\tau S_2 \sigma$ 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 regarding the comparison of topologies.
Keywords
Spaces with more topologies, separation axioms in bitopological spaces, $\theta$-regularity, pairwise paracompactness
Authors
RIV year
2001
Released
1. 1. 2001
ISBN
0161-1712
Periodical
International Journal of Mathematics and Mathematical Sciences
Year of study
26
Number
4
State
Czech Republic
Pages from
233
Pages to
237
Pages count
5
BibTex
@article{BUT40135, author="Martin {Kovár}", title="A note on the comparison of topologies", journal="International Journal of Mathematics and Mathematical Sciences", year="2001", volume="26", number="4", pages="5", issn="0161-1712" }