FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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
$\tau_q\subseteq \tau$ there is a pseudometric $p$ on $X$ such
that $\tau_q\subseteq \tau_p\subseteq \tau$ .
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