• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.385-389
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• 2015

In this paper we introduce the notions of expansiveness and measure expansiveness for homeomorphisms on a compact metric space, and we study the measure expansiveness of circle homeomorphisms.

• 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 Korean Mathematical Society
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• v.59 no.5
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• pp.987-996
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• 2022

We introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable compact spaces which are generalizations of expansivity and shadowing, respectively, for metric spaces. The main result is to generalize the Smale's spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.645-650
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• 2008

Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the $C^0$ topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.449-457
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• 2020

The aim of this short paper is to show some rigidity results for the actions of certain finitely presented groups by homeomorphisms. As an interesting and special case, we show that the actions of Higman-Thompson groups by homeomorphisms on a cohomology manifold with a non-zero Euler characteristic should be trivial. This is related to the wellknown Zimmer program and shows that the actions by homeomorphism could be very much different from those by diffeomorphisms.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.397-416
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• 2016

This paper is devoted to the study of various notions of almost openness and almost homeomorphisms and the characterization of some of them in terms of the relative interior operator. Generally, openness (or quasi-openness) for a continuous map f is well known. We define openness (or quasi-openness) at a point x using the relative interior operator and characterize that a continuous map f is almost open, almost quasi-open, almost embedding and almost homeomorphsims.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.329-333
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• 2022

In this paper we investigate some properties concerning the set of shadowable points for homeomorphisms. Then we show that the almost shadowing property is preserved by a topological conjugacy between homeomorphisms. Also, we give an example to illustrate our results.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1299-1307
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• 2023

In this paper, we attempt to study several topological properties for the function space H(X), space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at X compact. Furthermore, we prove that the space H(X) endowed with the regular topology is a topological group when X is a metric, almost P-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on ℝ under regular topology are open subspaces of H(ℝ) and are homeomorphic.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.759-764
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• 2004

Let X = {a} ${\cup}$ {$a_{i}$ ${$\mid$}$i $\in$ N} be a subspace of Euclidean space $E^2$ such that $lim_{{i}{\longrightarrow}{$\infty}}a_{i}$ = a and $a_{i}\;{\neq}\;a_{j}$ for $i{\neq}j$. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y) of all homeomorphisms on Y, where Y = {a, b} ${\cup}$ {$a_{i}{$\mid$}i{\in}Z$} is a subspace of $E^2$ such that $lim_{i}$-$\infty$ $a_{i}$ = b and $lim_{{i}{\longrightarrow}{$\infty}}a_{i}$ = a with the following properties; $a_{i}{\neq}a_{j}$ for $i{\neq}j$ and $a{\neq}b$.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.519-529
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• 2004

M. Brown [2] posed an open question on the class of free homeomorphisms as follows: if f is a free homeomorphism of two manifold and k is a positive integer then is $f^{k}$ free\ulcorner In this paper we show that the answer of the open question is true.