Topological stability in hyperspace dynamical systems
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1309-1318
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.
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