Geodesic
Some conditions under which a uniform space is fine
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 543-547.

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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.
Classification : 54A25, 54A35, 54E15
Keywords: uniform space; uniform weight; fine uniformity; uniformly locally finite; $\omega _\mu $-additive space; $\omega _\mu $-metric space 
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     title = {Some conditions under which a uniform space is fine},
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Marconi, Umberto. Some conditions under which a uniform space is fine. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 543-547. http://geodesic.mathdoc.fr/item/CMUC_1993__34_3_a16/