Some notes on induced functions and group actions on hyperspaces

2021/04/26 by Victor Donjuán, Donjuán, Victor, Natalia Jonard-Pérez +3 · 1 citation
Computer Science · Mathematics · #54B20 #54C05 #54C35 #54H15 #57S05 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2104.12904

openalex publication_date 2021/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the problem of when a continuous map between topological spaces induces a continuous function between their respective hyperspaces. We characterize the continuity of the induced function in the case of the Fell and Attouch-Wets hyperspaces. Additionally we explore the problem of whether a continuous action of a topological group G on a topological space X induces a continuous action on CL(X).

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