Let $X$ be a uniform space of uniform weight $\mu$. It is shown that if every open covering, of power at most $\mu$, is uniform, then $X$ is fine. Furthermore, an $\omega _\mu $-metric space is fine, provided that every finite open covering is uniform.
@article{118611,
author = {Umberto Marconi},
title = {Some conditions under which a uniform space is fine},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {34},
year = {1993},
pages = {543-547},
zbl = {0845.54017},
mrnumber = {1243086},
language = {en},
url = {http://dml.mathdoc.fr/item/118611}
}
Marconi, Umberto. Some conditions under which a uniform space is fine. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 543-547. http://gdmltest.u-ga.fr/item/118611/
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