• 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 [?].

• East Asian mathematical journal
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• v.18 no.1
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• pp.147-154
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• 2002

In this paper, we prove a few coincidence point theorems for two pairs of mappings in $T_1$ topological spaces. Our results extend, improve and unify the corresponding results in [1]-[3].

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.1-18
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.247-262
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• 2024

In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space X, a syndetically transitive semiflow (T, X, 𝜋) having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a T₃ space X, a transitive, nonminimal semiflow (T, X, 𝜋) having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.19-27
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• 1995

In 1974 H.Herrlich invented nearness spaces, a very fruitful concept which enables one to unify topological aspects. In this paper, we introduce the Lindel$\ddot{o}$f nearness structure, countably bounded nearness structure and countably totally bounded nearness structure. And we show that (X, ${\xi}_L$) is concrete and complete if and only if ${\xi}_L={\xi}_t$ in a symmetric topological space (X, t). Also we show that the following are equivalent in a symmetric topological space (X, t): (1) (X, ${\xi}_L$) is countably totally bounded. (2) (X, ${\xi}_t$) is countably totally bounded. (3) (X, t) is countably compact.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.53-69
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• 2013

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.79-84
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• 2022

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T₁-connected fuzzy topological spaces.

• East Asian mathematical journal
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• v.22 no.2
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• pp.131-149
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• 2006

In this paper we introduce the concept of $\gamma$-preopen sets in a topological space together with its corresponding $\gamma$-preclosure and $\gamma$-preinterior operators and a new class of topology $\tau_{{\gamma}p}$ which is generated by the class of $\gamma$-preopen sets. Also we introduce $\gamma$-pre $T_i$ spaces(i=0, $\frac{1}{2}$, 1, 2) and study some of its properties and we proved that if $\gamma$ is a regular operation, then$(X,\;{\tau}_{{\gamma}p})$ is a $\gamma$-pre $T\frac{1}{2}$ space. Finally we introduce $(\gamma,\;\beta)$-precontinuous mappings and study some of its properties.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.95-97
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• 1983

In this paper, we show a necessary and sufficient condition for QHC spaces to be S-closed. T. Thomson introduced S-closed spaces in [2]. A topological space X is said to be S-closed if every semi-open cover of X admits a finite subfamily such that the closures of whose members cover the space, where a set A is semi-open if and only if there exists an open set U such that U.contnd.A.contnd.Cl U. A topological space X is quasi-H-closed (denote QHC) if every open cover has a finite subfamily whose closures cover the space. If a topological space X is Hausdorff and QHC, then X is H-closed. It is obvious that every S-closed space is QHC but the converse is not true [2]. In [1], Cameron proved that an extremally disconnected QHC space is S-closed. But S-closed spaces are not necessarily extremally disconnected. Therefore we want to find a necessary and sufficient condition for QHC spaces to be S-closed. A topological space X is said to be semi-locally S-closed if each point of X has a S-closed open neighborhood. Of course, a locally S-closed space is semi-locally S-closed.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.323-338
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• 2011

In this paper, we introduce ($$\tilde{g}$$, s)-continuous functions between topological spaces, study some of its basic properties and discuss its relationships with other topological functions.