Topological stability in hyperspace dynamical systems Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1309-1318 https://doi.org/10.4134/CKMS.c200058 Published online September 14, 2020 Printed October 31, 2020 Namjip Koo, Hyunhee Lee, Nyamdavaa Tsegmid Chungnam National University; Chungnam National University; Mongolian National University of Education Abstract : In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable. Keywords : Hyperspace, the induced map, topological stability, expansiveness, shadowing property MSC numbers : Primary 54B20, 37C50, 37C75, 37C70 Supported by : The first author was supported by the National Research Foundations of Korea(NRF) grant funded by the Korea government(MSIT)(No.2020R1F1A1A01068032). The third author was supported by research fund of Mongolian National University of Education. Downloads: Full-text PDF   Full-text HTML