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On $theta$-regular Spaces

KOVÁR, M. On $theta$-regular Spaces. INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES, 1994, vol. 17, no. 4, 6 p. ISSN: 0161-1712.
Type
journal article
Language
English
Authors
Abstract

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.

Keywords

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

Published
1994
Pages
6
Journal
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES, vol. 17, no. 4, ISSN 0161-1712
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"
}
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