Detail publikace

On $theta$-regular Spaces

KOVÁR, M.

Originální název

On $theta$-regular Spaces

Anglický název

On $theta$-regular Spaces

Jazyk

en

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.

Dokumenty

BibTex


@article{BUT40079,
  author="Martin {Kovár}",
  title="On $theta$-regular Spaces",
  annote="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.
",
  chapter="40079",
  number="4",
  volume="17",
  year="1994",
  month="january",
  pages="687",
  type="journal article - other"
}