• 대한수학회논문집
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• 제13권3호
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• pp.595-601
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• 1998

In this paper we construct a homeomorphism on a Cantor set which is nearly periodic such that h(a) = b for given a, b $\in$ D$_{p}$. We also give an example which is not almost periodic and we discuss when a homeomorphism on a Cantor set is periodic.c.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권1호
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• pp.13-16
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• 1998

For continuous maps f of the circle to itself, we show that (1) every $\omega$-limit point is recurrent (or almost periodic) if and only if every $\omega$-limit set is minimal, (2) every $\omega$-limit set is almost periodic, then every $\omega$-limit set contains only one minimal set.

• 충청수학회지
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• 제20권4호
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• pp.477-484
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• 2007

Let h : M ${\rightarrow}$ M be an almost periodic homeomorphism of a compact metric space M onto itself. We prove that h is topologically transitive iff every element of M has a dense orbit. It follows as a corollary that an almost periodic homeomorphism of a compact metric space onto itself can not be chaotic. Some additional related observations on a Cantor set are made.

• 대한수학회논문집
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• 제15권3호
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• pp.549-553
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• 2000

For a continuous map of the circle to itself, we give necessary and sufficient conditions for the $\omega$-limit set of each nonwandering point to be minimal.

• 대한수학회보
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• 제31권2호
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• pp.187-192
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• 1994

The author extended the small properties of topological semilattices to that of regular semigroups [3]. In this paper, it could be shown that a semigroup S is almost regular if and only if over bar RL = over bar R.cap.L for every right ideal R and every left ideal L of S. Moreover, it has shown that the Bohr compactification of an almost regular semigroup is regular. Throughout, a semigroup will mean a topological semigroup which is a Hausdorff space together with a continuous associative multiplication. For a semigroup S, we denote E(S) by the set of all idempotents of S. An element x of a semigroup S is called regular if and only if x .mem. xSx. A semigroup S is termed regular if every element of S is regular. If x .mem. S is regular, then there exists an element y .mem S such that x xyx and y = yxy (y is called an inverse of x) If y is an inverse of x, then xy and yx are both idempotents but are not always equal. A semigroup S is termed recurrent( or almost pointwise periodic) at x .mem. S if and only if for any open set U about x, there is an integer p > 1 such that x$^{p}$ .mem.U.S is said to be recurrent (or almost periodic) if and only if S is recurrent at every x .mem. S. It is known that if x .mem. S is recurrent and .GAMMA.(x)=over bar {x,x$^{2}$,..,} is compact, then .GAMMA.(x) is a subgroup of S and hence x is a regular element of S.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제3권2호
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• pp.123-129
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• 1996

In this paper, we investigate the properties of various limit sets. In particular, we study the relationship between the recurrent set and special $\gamma$-limit set. And also we show that if $\chi$ is not almost periodic, then $\chi$ is special a-limit.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2001년도 봄 학술발표회 논문집
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• pp.699-706
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• 2001

Waterproofing materials should be expected to last the life of the structure. An approximate life cycle cost should be to compare different materials based on initial and periodic repair / maintenance costs. Waterproofing applicators like materials that are easy to set up and clean up. The designer should choose a material that can be applied in almost all conditions. Design Professionals should specify independent inspection on critical jobs or in all cases where the budget permits. The basic causes of defection occurred during construction should be minimized.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.277-288
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• 2004

In this paper, we discuss a continuous self-map of an interval and the existence of an uncountable strongly chaotic set. It is proved that if a continuous self-map of an interval has positive topological entropy, then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.

• 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.