Detail výsledku
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 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.
Spaces with more topologies, separation axioms in bitopological spaces, $\theta$-regularity,
pairwise paracompactness
@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"
}