On a class of hereditarily paracompact spaces

H. A. Kunzi ; S. Watson ; H. Junnila

Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 1, pp. 141-154

Résumé

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.