On zero-dimensional spaces of closed subsets
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Abstract
In this paper, we study some basic properties related to separation axioms of the space of closed subsets of a zero-dimensional topological space.
Thus we characterize the hyperspace of a zero-dimensional topological space via the notions of normality and partition. Then we establish five equivalent conditions characterizing when the hyperspace of a compact Hausdorff space is zero-dimensional. Furthermore, we give some examples related to our results.
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