A note on hyperspaces and the compact-open topology

2014/12/13 by Federico Cantero Morán, Cantero, Federico
Mathematics · #54B20 #54C35 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1412.4249

openalex publication_date 2014/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the inclusion of map(X,Y) into map(K(X),K(Y)) is continuous, where K(X) is the space of non-empty compact subsets of X (also known as the hyperspace of compact subsets of X), and both spaces of maps are endowed with the compact-open topology.

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