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

Marconi, Umberto

Commentat. Math. Univ. Carol. 34, No. 3, 543-547 (1993).

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

Keywords:

fine uniformity; uniformly locally finite family; \(\omega_ \mu\)-additive space; uniform space; uniform weight; \(\omega_ \mu\)-metric space