• Honam Mathematical Journal
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• v.26 no.1
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• pp.107-117
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• 2004

The aim of this paper is to introduce a digital $({\kappa}_0,\;{\kappa}_1)$-covering map and a local $({\kappa}_0,\;{\kappa}_1)$-homeomorphism. And further, we show that a digital $({\kappa}_0,\;{\kappa}_1)$-covering map is a local $({\kappa}_0,\;{\kappa}_1)$-homeomorphism and the converse does not hold. Finally, some property of a digital covering map is investigated with relation to some restriction map. Furthermore, we raise an open problem with relation to the product covering map.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.923-952
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• 2008

In this paper several continuities and homeomorphisms in computer topology are studied and their applications are investigated in relation to the classification of subs paces of Khalimsky n-dimensional space $({\mathbb{Z}}^n,\;T^n)$. Precisely, the notions of K-$(k_0,\;k_1)$-,$(k_0,\;k_1)$-,KD-$(k_0,\;k_1)$-continuities, and Khalimsky continuity as well as those of K-$(k_0,\;k_1)$-, $(k_0,\;k_1)$-, KD-$(k_0,\;k_1)$-homeomorphisms, and Khalimsky homeomorphism are studied and further, their applications are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.409-415
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• 2006

In this paper, we study the condition that a given homeomorphism has a square root and give an example of a wandering homeomorphism without square roots.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.35-47
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• 1992

In this paper we give a necessary condition for a homeomorphism restricted to its nonwandering set to have the shadowing property. Also, we consider a homeomorphism which cannot have the shadowing property.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.403-409
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• 1999

In this paper we introduce the notions of expansive homeomorphism and its properties, and study the relation between countable compacta and ordinal numbers. Our results extend and improve those of T.Kimura and others.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.77-83
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• 2022

In this paper we investigate the topological stability of induced homeomorphisms on a hyperspace. More precisely, we show that an expansive induced homeomorphism on a hyperspace is topologically stable. We also give examples and a diagram about implications to illustrate our results.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.85-90
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• 2022

In this article, we consider the notion of expansiveness on compact metric spaces for symbolically point of view. And we show that a homeomorphism is symbolically countably expansive if and only if it is symbolically measure expansive. Moreover, we prove that a homeomorphism is symbolically N-expansive if and only if it is symbolically measure N-expanding.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.575-589
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• 2011

In order to examine the possibility of some topological structures into the fields of network science, telecommunications related to the future internet and a digitization, the paper studies the Marcus Wyse topological structure. Further, this paper develops the notions of lattice based Marcus Wyse continuity and lattice based Marcus Wyse homeomorphism which can be used for studying spaces $X{\subset}R^2$ in the Marcus Wyse topological approach. By using these two notions, we can study and classify lattice based simple closed Marcus Wyse curves.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.963-986
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• 2022

Given a dimension function 𝜔, we introduce the notion of an 𝜔-vector weighted digraph and an 𝜔-equivalence between them. Then we establish a bijection between the weakly (ℤ/2)ⁿ-equivariant homeomorphism classes of small covers over a product of simplices ∆^𝜔(1) × ⋯ × ∆^𝜔(m) and the set of 𝜔-equivalence classes of 𝜔-vector weighted digraphs with m-labeled vertices, where n is the sum of the dimensions of the simplicies. Using this bijection, we obtain a formula for the number of weakly (ℤ/2)ⁿ-equivariant homeomorphism classes of small covers over a product of three simplices.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.757-766
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• 2008

We define and characterize a fuzzy pairwise $\gamma$-irresolute open mapping (fuzzy pairwise $\gamma$-irresolute closed mapping) on a fuzzy bitopological space. We also characterize a fuzzy pairwise $\gamma$-irresolute homeomorphism on a fuzzy bitopological space.