• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.77-84
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• 2021

Let f : [0, 1] → [0, 1] be a multimodal map with positive topological entropy. The dynamics of the renormalization operator for multimodal maps have been investigated by Daniel Smania. It is proved that the measure of maximal entropy for a specific category of Cr interval maps is unique.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.373-382
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• 2006

In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}={f_i}\;\infty\limits_{i=1}$on circles is $h(f_{1,\infty})={\frac{lim\;sup}{n{\rightarrow}\infty}}\;\frac 1 n \;log\;{\prod}\limits_{i=1}^n|deg\;f_i|$. As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism f on a smooth 2-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.57-59
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• 1997

The concept of fuzzy sets was introduced by Zad도 in his highly influential paper [5]. Using this concept, Chang [1] introduced a notion of fuzzy topological spaces which formally is the same one as for ordinary topological spaces. Observing that with Chang's definition constant maps between fuzzy topological spaces are not necessarily continuous, Lowen [2] gave an alternative and more natural definition for a fuzzy topological spaces and characterized the fuzzy compact spaces by means of prefilters in [4]. In this paper we give new characterizations of fuzzy compact spaces introduced in [2]. These results explain more clearly fuzzy compactness in fuzzy topological spaces.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.813-826
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• 2009

In this paper, we generalize the notions of preserving and strongly preserving maps to arbitrary set based topological categories. Further, we obtain characterizations of each of these concepts as well as interprete analogues and generalizations of theorems of Gerlits at al [20] in the categories of filter and local filter convergence spaces.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.617-633
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• 2002

In this paper, we study some properties of fuzzy interior spaces. Also, we investigate the relations between fuzzy interior spaces and fuzzy topological spaces. In particular, we prove the existence of product fuzzy topological spaces and product fuzzy interior spaces. We investigate the relations between them.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.179-182
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• 2007

In this paper, we introduce the concepts of fuzzy (r, s)-semi-preopen sets and fuzzy (r, s)-semi-precontinuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. The relations among fuzzy (r, s)-semicontinuous, fuzzy (r, s)-precontinuous, and fuzzy (r, s)-semi-precontinuous maps are discussed. The concepts of fuzzy (r, s)-semi-preinterior, fuzzy (r, s)-semi-preclosure, fuzzy (r, s)-semi-preneighborhood, and fuzzy (r, s)-quasi-semi-preneighborhood are given. Using these concepts, the characterization for the fuzzy (r, s)-semi-precontinuous map is obtained. Also, we introduce the notions of fuzzy (r, s)-semi-preopen and fuzzy (r, s)-semi-preclosed maps on intuitionistic fuzzy topological spaces in Sostak's sense, and then we investigate some of their characteristic properties.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.38.3-38
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• 2002

$\textbullet$ The topological map using a thinning needs much simpler computation than that using a Voronoi. $\textbullet$ A thinning can provide much information on the environment (additional nodes). $\textbullet$ Each node created in a local map is considered as temporary and redundant nodes are discarded. $\textbullet$ A global topological map can be built fast and correctly through a thinning algorithm. $\textbullet$ Path planning can be easily achieved with a topological map.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.63-76
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• 2000

In this paper, we introduce the concept of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate the properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and show that the category of Chang's fuzzy topological spaces is a bireflective full subcategory of that of intuitionistic fuzzy topological spaces.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.177-183
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• 2004

In this paper, we introduce the concepts of half-interior, half-closure, half-gp-maps and half-gp-open maps defined by intuitionistic gradations of openness.

• Korean Journal of Mathematics
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• v.15 no.1
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• pp.27-37
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• 2007

In this paper, we introduce the concepts of r-semi-generalized fuzzy closed sets, r-semi-generalized fuzzy open sets, r-semi-generalized fuzzy continuous maps in fuzzy topological spaces and investigate some of their properties.