2025/05/10 by Ján Komara, Komara, Ján
Mathematics · #28A80 (Secondary) #54B20 (Primary) 54E35 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2505.06571
openalex publication_date 2025/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.