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Some cardinality properties of a hyperspace with the locally finite topology. (English) Zbl 0692.54002

The locally finite topology on a hyperspace is the natural generalization of the well-known Vietoris or finite topology. Recently some authors have investigated its properties finding interesting relationships with the Hausdorff metric topology, when the base space is metrizable, and the uniform topology, when the base space is normal. We are concerned with some cardinality properties of a hyperspace with the locally finite topology. Specifically we provide estimates of various cardinal functions defined on it.

MSC:

54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54B20 Hyperspaces in general topology
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