## Umberto Marconi

*Some conditions under which a uniform space is fine *

Comment.Math.Univ.Carolinae 34,3 (1993) 543-547. **Abstract:**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.

**Keywords:** uniform space, uniform weight, fine uniformity, uniformly locally finite, $\omega _\mu $-additive space, $\omega _\mu $-metric space

**AMS Subject Classification:** Primary 54E15; Secondary 54A25, 54A35

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