• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.569-581
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• 2011

Let a finite group R act smoothly on a closed manifold M. We assume that R acts freely on M except a union of closed submanifolds with codimension at least two. Then, we show that there exists an isomorphism between equivariant topological complex vector bundles over M and nonequivariant topological complex vector orbibundles over the orbifold M/R. By using this, we can classify nonequivariant vector orbibundles over the orbifold especially when the manifold is two-sphere because we have classified equivariant topological complex vector bundles over two sphere under a compact Lie group (not necessarily effective) action in [6]. This classification of orbibundles conversely explains for one of two exceptional cases of [6].

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.22 no.8
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• pp.573-578
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• 2010

Topological matrix which reflects characteristics of network connectivity has been widely used in efficient solving for complicated flow network. Using topological matrix, one can easily define continuity at each node of flow network and make algorithm to automatically generate continuity equation of matrix form. In order to analyze flow network completely it is required to satisfy energy conservation in closed loops of flow network. Fundamental cycle retrieving algorithm based on graph theory automatically constructs energy conservation equation in closed loops. However, it is often accompanied by NP-complete problem. In addition, it always needs fundamental cycle retrieving procedure for every structural change of flow network. This paper proposes alternative mathematical method to analyze flow network without fundamental cycle retrieving algorithm. Consequently, the new mathematical method is expected to reduce solving time and prevent error occurrence by means of simplifying flow network analysis procedure.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.39-52
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• 2019

The aim of this paper is to introduce the notions of (quasi) weakly almost periodic point, measure center and minimal center of attraction of amenable group actions, explore the connections of levels of the orbit's topological structure of (quasi) weakly almost periodic points and study chaotic dynamics of transitive systems with full measure centers. Actually, we showed that weakly almost periodic points and quasiweakly almost periodic points have distinct orbit's topological structure and proved that there exists at least countable Li-Yorke pairs if the system contains a proper (quasi) weakly almost periodic point and that a transitive but not minimal system with a full measure center is strongly ergodically chaotic.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.437-443
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• 2006

We study free actions of finite groups on the 3-dimensional nilmanifold for Type 1 and classify all such group actions, up to topological conjugacy. This work supplies missing one in [1, Theorem 3.11.].

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.223-230
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• 2007

We study free actions of finite groups on the 3-dimensional nilmanifold and classify all such group actions, up to topological conjugacy. This work generalize Theorem 3.10 of [1].

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.223-232
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• 2005

We study only free actions of finite groups G on the 3-dimensional nilmanifold, up to topological conjugacy which yields an infra-nilmanifold of type 2.

• Kyungpook Mathematical Journal
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• v.9 no.1_2
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• pp.63-65
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• 1969

• Journal of the Korean Mathematical Society
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• v.14 no.1
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• pp.93-98
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• 1977

• 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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.333-346
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• 2002

Let $F={F^v:S^1->S^1,v\in\; V$ and $g={G^v:S^1->S^1,v\in\; V$ be disjoint flows defined on the unit circle $S^1$, that is such flows that each their element either is the identity mapping or has no fixed point ((V, +) is a 2-divisible nontrivial abelian group). The aim of this paper is to give a necessary and sufficient codition for topological conjugacy of disjoint flows i.e., the existence of a homeomorphism $\Gamma:S^1->S^1$ satisfying $$\Gamma\circ\ F^v=G^v\circ\Gamma,\; v\in\; V$$ Moreover, under some further restrictions, we determine all such homeomorphisms.