Result Details
On $theta$-regular Spaces
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.
$\theta$-regularity, (point) (countable) (semi-)paracompactness, covers,
filter bases, nets, $\theta$-closure, $\theta$-cluster point
@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"
}