Detail publikačního výsledku

On $theta$-regular Spaces

KOVÁR, M.

Originální název

On $theta$-regular Spaces

Anglický název

On $theta$-regular Spaces

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

In this paper we study $\theta$-regularity and its relations to other topological properties. We show that the concepts of $\theta$-regularity (Jankovi\'c, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces are $\theta$-regular. We discuss the problem when a (countably) $\theta$-regular space is regular, strongly locally compact, compact, or paracompact. We also study some basic properties of subspaces of a $\theta$-regular space. Some applications: A space is paracompact if{}f the space is countably $\theta$-regular and semiparacompact. A generalized $F_\sigma$-subspace of a paracompact space is paracompact if{}f the subspace is countably $\theta$-regular.

Anglický abstrakt

In this paper we study $\theta$-regularity and its relations to other topological properties. We show that the concepts of $\theta$-regularity (Jankovi\'c, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces are $\theta$-regular. We discuss the problem when a (countably) $\theta$-regular space is regular, strongly locally compact, compact, or paracompact. We also study some basic properties of subspaces of a $\theta$-regular space. Some applications: A space is paracompact if{}f the space is countably $\theta$-regular and semiparacompact. A generalized $F_\sigma$-subspace of a paracompact space is paracompact if{}f the subspace is countably $\theta$-regular.

Klíčová slova

$\theta$-regularity, (point) (countable) (semi-)paracompactness, covers, filter bases, nets, $\theta$-closure, $\theta$-cluster point

Klíčová slova v angličtině

$\theta$-regularity, (point) (countable) (semi-)paracompactness, covers, filter bases, nets, $\theta$-closure, $\theta$-cluster point

Autoři

KOVÁR, M.

Vydáno

01.01.1994

ISSN

0161-1712

Periodikum

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Svazek

17

Číslo

4

Stát

Spojené království Velké Británie a Severního Irska

Strany od

687

Strany počet

6

BibTex

@article{BUT40079,
  author="Martin {Kovár}",
  title="On $theta$-regular Spaces",
  journal="INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES",
  year="1994",
  volume="17",
  number="4",
  pages="6",
  issn="0161-1712"
}