• 대한수학회보
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• 제61권1호
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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.

• 충청수학회지
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• 제20권4호
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• pp.525-533
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• 2007

In this paper, we prove the continuity of the Zadeh extensions for continuous surjections and for semiflows.

• 충청수학회지
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• 제8권1호
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• pp.167-171
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• 1995

• 충청수학회지
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• 제5권1호
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• pp.49-56
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• 1992

• 충청수학회지
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• 제7권1호
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• pp.69-74
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• 1994

• 대한수학회지
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• 제54권3호
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• pp.773-791
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• 2017

In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.

• 충청수학회지
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• 제15권2호
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• pp.67-72
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• 2003

The purpose of this paper is to prove flow induced by a covering map. Lee and Park had studied semiflows induced by a covering map in 1997 [1]. This proof differs from the proof of Lee and Park. Notice that for the proof of this paper, we use the fact that $\mathbb{R}$ is connected space.