• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.14-17
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• 2003

By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

• 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}.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.157-160
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• 2005

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G\delta$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.259-269
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• 2021

We shall study the following. Let 𝜙 be an expansive flow on a compact TVS-cone metric space (X, d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space [?].

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.255-267
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• 2022

Uniform space is a generalization of metric space. The main purpose of this paper is to extend several results contained in [5, 6] which have for an expansive homeomorphism with the pseudo orbit tracing property(POTP in short) on a compact metric space (X, d) for an expansive homeomorphism with the POTP on a compact uniform space (X, 𝒰). we characterize stable and unstable sets, sink and source and saddle, recurrent points for an expansive homeomorphism which has the POTP on a compact uniform space (X, 𝒰).

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.152-156
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• 2010

We define some terminologies on intuitionistic fuzzy metric space and prove that the topology generated by any intuitionistic fuzzy metric space is metrizable. Also, we show that if the intuitionistic fuzzy metric space is complete, then the generated topology is completely metrizable, a Baire space, and that an intuitionistic fuzzy metric space is precompact if and only if every sequence has a Cauchy subsequence.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.735-747
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• 2018

Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.242-246
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• 2010

It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.931-941
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• 1995

The definitions and techniques, which deals with homotopic harmonic maps from a compact Riemannian manifold into a compact metric space, developed by N. J. Korevaar and R. M. Schoen [7] can be applied to more general situations. In this paper, we prove that for a complicated domain, possibly noncompact Riemannian manifold with infinitely generated fundamental group, the existence of homotopic harmonic maps can be proved if the initial map is simple in some sense.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.41-51
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• 2017

In this note, we deal with some characterizations of relative compactness on the $L_p$ metric space of fuzzy sets. And then, we point out that a characterization of relative compact subsets of fuzzy numbers with sendograph metric can be improved.