Topological stability for induced maps on a hyperspace Commun. Korean Math. Soc. Published online September 14, 2020 Namjip Koo, Hyunhee Lee, and Nyamdavaa Tsegmid Chungnam National University, Mongolian National University of Education Abstract : In this paper we expand 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 : 54B20, 37C50, 37C75, 37C70 Full-Text :