• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.665-676
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• 2004

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.293-298
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• 1994

It is well known that the approximation property and the compact approximation property are not hereditary properties; that is, a closed subspace M of a Banach space X with the (compact) approximation property need not have the (compact) approximation property. In 1973, A. Davie [2] proved that for each 2 < p < $\infty$, there is a closed subspace $Y_{p}$ of $\ell_{p}$ which does not have the approximation property. In fact, the space Davie constructed even fails to have a weaker property, the compact approximation property. In 1991, A. Lima [12] proved that if X is a Banach space with the approximation property and a closed subspace M of X is locally $\lambda$-complemented in X for some $1\leq\lambda < $\infty$, then M has the approximation property.(omitted)

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.157-163
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• 2020

Conley introduced attracting sets and repelling sets for a flow on a topological space and showed that if f is a flow on a compact metric space, then 𝓡(f) = ⋂{A_U ∪ A*_U |U is a trapping region for f}. In this paper we introduce chain recurrent set, trapping region, attracting set and repelling set for a flow f on a TVS-cone metric space and prove that if f is a flow on a compact TVS-cone metric space, then 𝓡(f) = ⋂{A_U ∪ A*_U |U is a trapping region for f}.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.171-179
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• 2000

We prove the following: (1) For a Hausdorff space X, the hyperspace K(X) of compact subsets of X is hemicompact if and only if X is hemicompact. (2) For a regular space X, the hyperspace $C_K(X)$ of subcontinua of X is hemicompact (hemiconnected) if and only if X is hemicompact (hemiconnected). (3) For a locally compact Hausdorff space X, each open set in X is hemicompact if and only if each basic open set in the hyperspace K(X) is hemicompact. (4) For a connected, locally connected, locally compact Hausdorff space X, K(X) is hemiconnected if and only if X is hemiconnected.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1125-1135
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• 2018

We show that for an M-action on a compact Hausdorff uniform space, if it has at least two disjoint compact invariant subsets, then it is thickly syndetically sensitive. Additionally, we point out that for a P-M-action of a discrete abelian group on a compact Hausdorff uniform space, the multi-sensitivity is equivalent to both thick sensitivity and thickly syndetic sensitivity.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.197-200
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• 2012

Concerning the integrability of almost K$\ddot{a}$hler manifolds, we prove that a compact almost K$\ddot{a}$hler locally symmetric space is K$\ddot{a}$hler if the length of the star Ricci tensor is not smaller than that of the Ricci tensor.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.397-410
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• 2002

In this paper, some inequalities for vector-valued maximal functions over locally compact Vienkin groups are obtained.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.307-313
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• 2005

The Lefschetz fixed point theorem is extended to compact continuous maps defined on an admissible subset of a Hausdorff topological space.

• 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.

• The Mathematical Education
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• v.13 no.3
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• pp.17-18
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• 1975

거리공간과 Normal countable compact의 위상적이 Normal이라는 것은 A.H. Stone에 의하여 이미 밝혀졌고, V.I. Malyhin은 space expX의 Cardrmal invariant와 공간 X 사이의 관계를 논하였다. 본 논문에서는 V.I. Malyin이 밝힌 tightness의 개념을 도입하여 countable tightness의 pracompact와 normal strongly countable compact 공간의 topological product가 Normal이라는 것을 증명하였다.