• 호남수학학술지
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• 제32권1호
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• pp.141-155
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• 2010

In this paper we prove that with some hypothesis the set of k-isomorphism classes of simple closed k-surfaces in ${\mathbf{Z}}^3$ forms a commutative monoid with an operation derived from a digital connected sum, k ${\in}$ {18,26}. Besides, with some hypothesis the set of k-homotopy equivalence classes of closed k-surfaces in ${\mathbf{Z}}^3$ is also proved to be a commutative monoid with the above operation, k ${\in}$ {18,26}.

• 대한수학회지
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• 제44권6호
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.

• 호남수학학술지
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• 제34권3호
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• pp.451-465
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• 2012

Since there are several kinds of continuities of maps between digital spaces, the paper compares them, which can play an important role in digital topology and discrete geometry.

• 호남수학학술지
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• 제29권1호
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• pp.101-118
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• 2007

The notions of digital k-homotopy equivalence and digital ($k_0,k_1$)-homotopy equivalence were developed in [13, 16]. By the use of the digital k-homotopy equivalence, we can investigate digital k-homotopy equivalent properties of Cartesian products constructed by the minimal simple closed 4- and 8-curves in $\mathbf{Z}^2$.

• 디지털융복합연구
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• 제17권1호
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• pp.43-53
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• 2019

이 연구는 국내 대학 소속 교수학습개발센터(CTL)의 운영과정을 신제도주의 동형화 이론을 바탕으로 고찰하는데 목적이 있다. 신제도주의자들은 조직의 구조와 행동이 조직의 자율적, 합리적 선택이라기보다는 사회에서 인정되는 가치와 규범을 반영하는 것으로 본다. 광범위한 선행연구와 관련 문헌연구 방법을 통해 그리고 동형화 이론적 틀을 바탕으로 CTL의 도입 및 확산, 제도화 과정을 분석한 결과, 국내 대학 CTL의 도입 및 확산 과정에서는 정부 주관의 강제적 동형화와 대학 간 상호 모방 효과가 상대적으로 크게 작동하였다. 또한 전문협의체인 대학교육개발센터협의회는 규범적 동형화의 직접적인 주체로서 핵심적인 역할을 수행하였다. 즉, 국내 대학 CTL은 환경에 대한 외적 정당성 확보를 위한 과정으로 볼 수 있고, 특히 대학은 정부의 평가 기준에 순응 및 동조하면서 조직 형태를 동형화시켰음을 확인할 수 있었다. 급변하는 대학교육 환경의 변화에 대응하여 CTL이 주도적으로 대학교육 발전의 엔진이 될 수 있도록 고유한 가치와 전략을 개발하고 이를 대학 실정에 맞게 발전시키는 노력이 필요하다.

• 호남수학학술지
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• 제32권3호
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• pp.375-387
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• 2010

The paper studies an existence problem of a (generalized) universal covering space over a digital wedge with a compatible adjacency. In algebraic topology it is well-known that a connected, locally path connected, semilocally simply connected space has a universal covering space. Unlike this property, in digital covering theory we need to investigate its digital version which remains open.

• 호남수학학술지
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• 제30권2호
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• pp.207-217
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• 2008

Digital geometry has strongly contributed to the study of a discrete topological space $X{\subset}{\mathbf{Z}}^n$ with k-adjacency of ${\mathbf{Z}}^n$. As a survey-type article, we review various utilities of digital geometry.

• 호남수학학술지
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• 제30권4호
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.

• 호남수학학술지
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• 제36권1호
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• pp.199-215
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• 2014

Owing to the development of the notion of normal adjacency of a digital product [9], product properties of digital topological properties were studied efficiently. To equivalently represent a normal adjacency of a digital product, the present paper proposes an S-compatible adjacency of a digital product. This approach can be helpful to understand a normal adjacency of a digital product. Finally, using an S-compatible adjacency of a digital product, we can study product properties of digital topological properties, which improves the presentations of the normal adjacency of a digital product in [9] and [5, 6].

• 호남수학학술지
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• 제31권3호
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• pp.279-292
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• 2009

As a survey-type article, the paper reviews some results on a regular covering space in digital covering theory. The recent paper [10](see also [12]) established the notion of regular covering space in digital covering theory and studied its various properties. Besides, the papers [14, 16] developed a discrete Deck's transformation group of a digital covering. In this paper we study further their properties. By using these properties, we can classify digital covering spaces. Finally, the paper proposes an open problem.