Topologically stable points and uniform limits

Namjip Koo; Hyunhee Lee

doi:10.4134/JKMS.j220595

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2023; 60(5): 1043-1055

Online first article August 22, 2023 Printed September 1, 2023

https://doi.org/10.4134/JKMS.j220595

Topologically stable points and uniform limits

Namjip Koo, Hyunhee Lee

Chungnam National University; Chungnam National University

Abstract

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Abstract

In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.

Keywords: Shadowable point, uniformly expansive point, topologically stable point, uniform limit, closable point

MSC numbers: Primary 37B25, 37C15, 37C50

Supported by: This work was supported by the National Research Foundations of Korea(NRF) grant funded by the Korea government(MSIT)(No.2020 R1F1A1A01068032). The second was supported by the National Research Foundations of Korea(NRF) grant funded by the Korea government(MSIT)(No. 2021R1A6A3A13039168).