Detail publikačního výsledku

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

Druh

Článek recenzovaný mimo WoS a Scopus

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.

Klíčová slova

Spaces with more topologies, separation axioms in bitopological spaces, $\theta$-regularity, pairwise paracompactness

Klíčová slova v angličtině

Spaces with more topologies, separation axioms in bitopological spaces, $\theta$-regularity, pairwise paracompactness

Autoři

KOVÁR, M.

Vydáno

01.01.2001

ISSN

0161-1712

Periodikum

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Svazek

26

Číslo

4

Stát

Spojené království Velké Británie a Severního Irska

Strany od

233

Strany počet

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"
}