Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2020; 35(4): 1309-1318

Online first article September 14, 2020      Printed October 31, 2020

https://doi.org/10.4134/CKMS.c200058

Copyright © The Korean Mathematical Society.

Topological stability in hyperspace dynamical systems

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.