Some base axioms for topology involving enumerability
Aull, C. E.
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Displaying similar documents to “Metrizability of spaces with countably based closed sets”
Some base axioms for topology involving enumerability
On countably paracompact spaces and closed maps
Harley, P.W. III (1989)
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Upper semicontinuous decompositions of spaces having bases of countable order
Worrell, J.M. jr. (1967)
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A lattice of conditions on topological spaces II
P. Moody, G. Reed, A. Roscoe, P. Collins (1991)
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On the metrizability of -spaces and its relationship to the normal Moore space conjecture
Z. Balogh (1981)
Fundamenta Mathematicae
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Addition theorems and -spaces
Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is proved that if a regular space is the union of a finite family of metrizable subspaces then is a -space in the sense of E. van Douwen. It follows that if a regular space of countable extent is the union of a finite collection of metrizable subspaces then is Lindelöf. The proofs are based on a principal result of this paper: every space with a point-countable base is a -space. Some other new results on the properties of spaces which are unions of a finite collection of...