• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.95-101
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• 2020

In this paper we introduce the notion of the expansivity for homeomorphisms on a compact metric space and study some properties concerning weak expansive homeomorphisms. Also, we give some examples to illustrate our results.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.157-164
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• 2019

In this article, we study expansiveness of the shift maps on orbital inverse limit spaces which consist of two cross bonding mappings. On orbital inverse limit systems, horizontal directions express inverse limit systems and vertical directions mean orbits based on horizontal axes. We characterize the c-expansiveness of functions on orbital spaces. We also prove that the c-expansiveness of the functions is equivalent to the expansiveness of the shift maps on orbital inverse limit spaces.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.319-343
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• 2022

We discuss the notions of positive expansivity, chain transitivity, uniform rigidity, chain mixing, weak specification, and pseudo orbital specification in terms of finite open covers for Hausdorff topological spaces and entourages for uniform spaces. We show that the two definitions for each notion are equivalent in compact Hausdorff spaces and further they are equivalent to their standard definitions in compact metric spaces. We show that a homeomorphism on a Hausdorff uniform space has uniform h-shadowing if and only if it has uniform shadowing and its inverse is uniformly equicontinuous. We also show that a Hausdorff positively expansive system with a Hausdorff shadowing property has Hausdorff h-shadowing.