Addition theorems and $D$-spaces

Arhangel'skii, Aleksander V. ; Buzyakova, Raushan Z.

Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 653-663 / Harvested from Czech Digital Mathematics Library

Résumé

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 nice subspaces are obtained.

Détail

Publié le : 2002-01-01

MR 2045787 | Zbl 1090.54017

Classification:  54D20,  54E35,  54F99

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