• 대한수학회보
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• 제38권1호
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• pp.205-210
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• 2001

We give a characterization of regular operators that allows us to prove that a bounded operator acting between Banach spaces is almost regular if and only if it is regular, solving an open problem in [5]. As an application, we show that some operators in the closure of the set of all regular operators are regular.

• 호남수학학술지
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• 제41권3호
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• pp.449-461
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• 2019

The aim of this paper is to extend the concept of quasi and bi-ideals from left almost semigroups to left almost rings which are the generalization of one sided ideals. Further, we discuss quasi and bi-ideals in regular left almost rings and intra regular left almost rings. We then explore many interesting and elegant properties of quasi and bi-ideals.

• 대한수학회보
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• 제39권3호
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• pp.441-453
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• 2002

We introduce the concepts of fuzzy r-regular open sets and fuzzy almost r-continuous maps in the fuzzy topology of Chat-topadhyay. Also we investigate the equivalent conditions of the fuzzy almost r-continuity.

• 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.

• 한국지능시스템학회논문지
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• 제20권2호
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• pp.257-261
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• 2010

본 논문에서는 fuzzy r-generalized almost continuity의 개념과 특성을 연구한다. 특히 fuzzy r-generalized regular open sets를 이용하여 fuzzy r-generalized almost continuity의 특성을 밝힌다.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.364-369
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• 1998

In this paper, we introduce the notions of fuzzy ${\gamma}$-regular open sets and fuzzy almost ${\gamma}$-continuous maps, and investigate some of their basic properties.

• 충청수학회지
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• 제26권1호
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• pp.125-135
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• 2013

We introduce the concepts of fuzzy $(r,\;s)$-regular open sets and fuzzy almost $(r,\;s)$-continuous mappings on the intuitionistic fuzzy topological spaces in ${\check{S}}ostak^{\prime}s$ sense. Also we investigate the equivalent conditions of the fuzzy almost $(r,\;s)$-continuity.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제1권1호
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• pp.69-74
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• 2001

We introduce fuzzy semi-regular spaces. Furthermore, we investigate the relations among fuzzy super continuity, fuzzy $\delta$-continuity and fuzzy almost continuity in fuzzy topological spaces in view of the definition of Sostak. We study some properties between them.

• 산업기술연구
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• 제5권
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• pp.47-49
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• 1985

Semi-open을 기초로 하여 만들어진 S-closed 공간의 일반적인 성질을 살펴보고 S-closed 공간과 (maximum) filterbase와의 관계를 조사하였다. 이를 바탕으로 regular closed된 cover C, regular open set인 족(族) C, rc-accumulation, (maximum) filterbase에서의 관계(關係)를 살펴 보았다. Mapping theory에서 almost-open almost-continuous map f가 almost continuous되는 것을 보였다.

• 대한수학회보
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• 제59권5호
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• pp.1177-1190
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• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α₁, …, α_p and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and Ann_R(α^m) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αⁿ, bⁿ) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.