On θ-regular spaces

Abstract

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.

Keywords

• θ-regularity
• point paracompactness
• covers
• filter bases
• nets
• θ-closure
• θ-cluster point.