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On the infimum of the Hausdorff and Vietoris topologies. (English) Zbl 0845.54006
Summary: We study the infimum of the Hausdorff and Vietoris topologies on the hyperspace of a metric space. We show that this topology coincides with the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or is a UC space.

MSC:
54B20 Hyperspaces in general topology
54E35 Metric spaces, metrizability
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