Onθ-regular spaces
1994 ◽
Vol 17
(4)
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pp. 687-692
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Keyword(s):
In this paper we studyθ-regularity and its relations to other topological properties. We show that the concepts ofθ-regularity (Janković, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces areθ-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 aθ-regular space. Some applications: A space is paracompact iff the space is countablyθ-regular and semiparacompact. A generalizedFσ-subspace of a paracompact space is paracompact iff the subspace is countablyθ-regular.
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2012 ◽
Vol 11
(01)
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pp. 1250014
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Keyword(s):
1974 ◽
Vol 19
(2)
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pp. 125-132
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Keyword(s):
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2009 ◽
Vol 156
(7)
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pp. 1345-1347
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2019 ◽
Vol 2019
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pp. 1-7
2012 ◽
Vol 2012
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pp. 1-11
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2012 ◽
Vol 88
(1)
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pp. 12-16
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