On a problem of Tamano

Henry Potoczny

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Closure-preserving covers

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Addition theorems and $D$ -spaces

Aleksander V. Arhangel&#039;skii, Raushan Z. Buzyakova (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is proved that if a regular space $X$ is the union of a finite family of metrizable subspaces then $X$ is a $D$ -space in the sense of E. van Douwen. It follows that if a regular space $X$ of countable extent is the union of a finite collection of metrizable subspaces then $X$ is Lindelöf. The proofs are based on a principal result of this paper: every space with a point-countable base is a $D$ -space. Some other new results on the properties of spaces which are unions of a finite collection of...

A class of spaces whose Cartesian product with every hereditarily Lindelöf space in Lindelöf

K. Alster (1981)

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Displaying similar documents to “On a problem of Tamano”

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A class of spaces whose Cartesian product with every hereditarily Lindelöf space in Lindelöf

Addition theorems and $D$ -spaces