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Keywords:
uniform space; uniform weight; fine uniformity; uniformly locally finite; $\omega _\mu $-additive space; $\omega _\mu $-metric space
uniform space; uniform weight; fine uniformity; uniformly locally finite; $\omega _\mu $-additive space; $\omega _\mu $-metric space
Summary:
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.
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