On θ-regular spaces
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 (co...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171294000979 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |