Geodesic
On a~class of hereditarily paracompact spaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 1, pp. 141-154.

Voir la notice de l'article provenant de la source Math-Net.Ru

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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H. A. Kunzi; S. Watson; H. Junnila. On a~class of hereditarily paracompact spaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 1, pp. 141-154. http://geodesic.mathdoc.fr/item/FPM_1998_4_1_a11/