Publication detail

A note on the comparison of topologies

KOVÁR, M.

Original Title

A note on the comparison of topologies

English Title

A note on the comparison of topologies

Type

journal article - other

Language

en

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.

English 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

RIV year

2001

Released

01.01.2001

ISBN

0161-1712

Periodical

International Journal of Mathematics and Mathematical Sciences

Year of study

26

Number

4

State

CZ

Pages from

233

Pages to

237

Pages count

5

Documents

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"
}