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, τ ) is called upholstered provided that for any quasi-pseudometric q on X such that τ q ⊆ τ there is a pseudometric p on X such that τ 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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