On θ -regular spaces

Martin M. Kovár

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-6

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 F σ -subspace of a paracompact space is paracompact iff the subspace is countably θ -regular.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:423963

DOI: 10.1155/S0161171294000979

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