On completeness of Hausdorff hyperspaces
General Topology
2025-05-13 v1
Abstract
The Hausdorff hyperspace of a metric space consists of all its non-empty bounded closed sets and it is equipped with the Pompeiu--Hausdorff set distance. We present a simpler novel proof that the Hausdorff hyperspace of a complete space is complete as well. The Main Lemma is crucial in this demonstration and though it uses an induction argument -- the only one in our completeness proof -- it is stated purely in terms of neighborhoods.
Cite
@article{arxiv.2505.06571,
title = {On completeness of Hausdorff hyperspaces},
author = {Ján Komara},
journal= {arXiv preprint arXiv:2505.06571},
year = {2025}
}
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5 pages