## Some conditions under which a uniform space is fine.(English)Zbl 0845.54017

Summary: Let $$X$$ be a uniform space of uniform weight $$\mu$$. It is shown that if every open covering, the 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.

### MSC:

 54E15 Uniform structures and generalizations 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54A35 Consistency and independence results in general topology
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