FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 1, PAGES 181-186

Subnormal spaces and a Dowker-type problem

A. N. Yakivchik

Abstract

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In the present paper the class of subnormal spaces -- the spaces in which any two closed disjoint sets can be separated by disjoint $G$_δ sets -- is considered. It is proved that the product of a space $X$ by the closed real interval (or by any $\sigma$-compact Hausdorff space with countable network) is subnormal provided that $X$ is subnormal and countably metacompact. An example of a weakly normal space which is not subnormal is presented.

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Last modified: April 8, 1998