FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 1, PAGES 141-154

On a class of hereditarily paracompact spaces

H. Junnila
H.-P. A. Künzi
S. Watson

Abstract

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A topological space $(X,\; \tau \; )$ is called upholstered provided that for any quasi-pseudometric $q$ on $X$ such that $\tau$_q ⊆ τ there is a pseudometric $p$ on $X$ such that $\tau$_q ⊆ τ _p ⊆ τ. Each upholstered space is shown to be a perfect paracompact regular space and every perfect compact regular space is shown to be upholstered.

Each semi-stratifiable paracompact regular space is upholstered and each quasi-metrizable upholstered space is metrizable. The property of upholsteredness is preserved under closed continuous surjections.

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Last modified: April 8, 1998