Detail publikace

# A note on the comparison of topologies

KOVÁR, M.

Originální název

A note on the comparison of topologies

Anglický název

A note on the comparison of topologies

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Dokumenty

BibTex


@article{BUT40135,
author="Martin {Kovár}",
title="A note on the comparison of topologies",
annote="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.",
chapter="40135",
number="4",
volume="26",
year="2001",
month="january",
pages="233",
type="journal article - other"
}