• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.71-79
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• 2001

We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.253-258
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• 1996

For a nonelementary discrete group $\Gamma$ of hyperbolic isometries acting on $B^m(m\geq2)$, we give a topological characterization of conical limit points using admissible pairs.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.365-381
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• 2019

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_2$, up to topological conjugacy. We show that there exist three kinds of nonabelian group actions in ${\pi}_1$, two in ${\pi}_2$ or ${\pi}_{5,i}$(i = 1, 2, 3), one in the other cases, and clarify what those groups are.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.227-232
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• 2006

We study some dynamical properties in the context of bitransformation groups, and show that if (H,X,T) is a bitransformation group such that (H,X) is almost periodic and (X/H,T) is pointwise almost periodic $T_2$ and $x{\in}X$, then $E_x=\{q{\in}E(H,X){\mid}qx{\in}{\overline{xT}\}$ is a compact $T_2$ topological group and $E_{qx}=E_x(q{\in}E(H,X))$ when H is abelian, where E(H,X) is the enveloping semigroup of the transformation group (H,X).

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.509-524
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• 2019

Let Act(G, X) be the set of all continuous actions of a finitely generated group G on a compact metric space X. In this paper, we study the concepts of topologically stable points and continuous shadowable points of a group action T ∈ Act(G, X). We show that if T is expansive then the set of continuous shadowable points is contained in the set of topologically stable points.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.751-763
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• 2016

The properties of the nonabelian tensor products are interesting in different contexts of algebraic topology and group theory. We prove two theorems, dealing with the nonabelian tensor products of projective limits of finite groups. The first describes their topology. Then we show a result of embedding in the second homology group of a pro-p-group, via the notion of complete exterior centralizer. We end with some open questions, originating from these two results.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.1
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• pp.223-229
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• 2018

This paper proposes a robust technique of image segmentation, which can be obtained if the topological persistence of each connected component is used as the feature vector for the graph-based image segmentation. The topological persistence of the components, which are obtained from the super-level set of the image, is computed from the morse function which is associated with the gray-level or color value of each pixel of the image. The procedure for the components to be born and be merged with the other components is presented in terms of zero-dimensional homology group. Extensive experiments are conducted with a variety of images to show the more correct image segmentation can be obtained by merging the components of small persistence into the adjacent components of large persistence.

• Journal of the Korean Institute of Telematics and Electronics
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• v.12 no.2
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• pp.11-17
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• 1975

The paper examined the character structure as a basic study for the recognition of Korean characters. In view of concave structure, line structure and node relationship of character graph, the algebraic structure of the basic Korean characters is are analized. Also, the degree of complexities in their character structure is discussed and classififed. Futhermore, by describing the fact that some equivalence relations are existed between the 10 vowels of rotational transformation group by Affine transformation of one element into another, it could be pointed out that the geometrical properting in addition to the topological properties are very important for the recognition of Korean characters.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.161-175
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• 1997

We classify free actions of finite abelian groups on the 3-dimensional nilmanifold, up to topological conjugacy. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.481-485
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• 1996

Let G be an abelian topological group and $x_{ij} \in G$ for all $i, j \in N$ such that the series $\sum_{j=i}^{\infty} x_{ij}$ is subseries convergent for each i.