International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 687-692

On θ-regular spaces

Martin M. Kovár

Department of Mathematics, Faculty of Electrical Engineering, Technical University of Brno, Areál VUT, Kraví Hora 21/XV, Brno 602 00, Czech Republic

Received 16 June 1993

Copyright © 1994 Martin M. Kovár. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we study θ-regularity and its relations to other topological properties. We show that the concepts of θ-regularity (Janković, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces are θ-regular. We discuss the problem when a (countably) θ-regular space is regular, strongly locally compact, compact, or paracompact. We also study some basic properties of subspaces of a θ-regular space. Some applications: A space is paracompact iff the space is countably θ-regular and semiparacompact. A generalized Fσ-subspace of a paracompact space is paracompact iff the subspace is countably θ-regular.