Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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TOPOLOGICALLY STABLE POINTS AND UNIFORM LIMITS

  • Namjip Koo (Department of Mathematics Chungnam National University) ;
  • Hyunhee Lee (Department of Mathematics Chungnam National University)
  • Received : 2022.12.01
  • Accepted : 2023.03.02
  • Published : 2023.09.01
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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.

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Acknowledgement

This work was supported by the National Research Foundations of Korea(NRF) grant funded by the Korea government(MSIT)(No.2020R1F1A1A01068032). The second was supported by the National Research Foundations of Korea(NRF) grant funded by the Korea government(MSIT)(No. 2021R1A6A3A13039168). The authors are grateful to the refree for the comments on the previous version of this paper.

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