• 대한수학회논문집
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• 제30권3호
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• pp.277-282
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• 2015

We obtain some conditions for disconnectedness of a topological space in terms of maximal and minimal open sets, and some similar results in terms of maximal and minimal closed sets along with interrelations between them. In particular, we show that if a space has a set which is both maximal and minimal open, then either this set is the only nontrivial open set in the space or the space is disconnected. We also obtain a result concerning a minimal open set on a subspace.

• 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.

• Journal of the Korean Statistical Society
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• 제29권3호
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• pp.297-306
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• 2000

An efficient method of constructing $textsc{k}$-minimal path sets to evaluate the reliability of a flow network is presented. The network is considered to be in a functioning state if it can transmit a maximum flow which is greater than or equal to a specified amount of flow, $textsc{k}$say, and a $textsc{k}$-minimal path set is a minimal set of branches that satisfies the given flow constraint. In this paper, under the assumption that minimal path sets of the network are known, we generate composite paths by adding only a minimal set of branches at each iteration to get $textsc{k}$-minimal path sets after possibly the fewest composition, and compute maximum flow of composite paths using only minimal path sets. Thereby we greatly reduce the possible occurrence of redundant composite paths throughout the process and efficiently compute the maximum flow of composite paths generated. Numerical examples illustrate the method.

• 충청수학회지
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• 제14권1호
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• pp.49-59
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• 2001

In this paper, we introduce an extended notion of regular homomorphism of minimal sets by considering a certain subgroup of the group of automorphisms of a universal minimal transfomation group.

• 대한수학회논문집
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• 제32권1호
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• pp.175-181
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• 2017

In this paper, we introduce a notion of cleanly covered topological spaces along with two strong separation axioms. Some properties of cleanly covered topological spaces are obtained in term of maximal open sets including some similar properties of a topological space in term of maximal closed sets. Two strong separation axioms are also investigated in terms of minimal open and maximal closed sets.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.251-257
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• 2021

This article is devoted to introduce the notion of fuzzy cleanly covered fuzzy topological spaces; in addition two strong fuzzy separation axioms are studied. By means of fuzzy maximal open sets some properties of fuzzy cleanly covered fuzzy topological spaces are obtained and also by means of fuzzy maximal closed sets few identical results of a fuzzy topological spaces are investigated. Through fuzzy minimal open and fuzzy maximal closed sets, two strong fuzzy separation axioms are discussed.

• Journal of Applied and Pure Mathematics
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• 제4권1_2호
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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.

• 한국지능시스템학회논문지
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• 제20권4호
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• pp.569-573
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• 2010

fuzzy r-minimal preopen set, fuzzy r-M precontinuous와 fuzzy r-M preopen 함수의 개념을 소개하며 특성들을 조사한다.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.891-897
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• 2002

A symmetric minimal complement at infinity for a given symmetric Silvester data set in the complex plane is contructed.

• Journal of Applied and Pure Mathematics
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• 제5권1_2호
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• pp.121-128
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• 2023

The aim of this article is to extend hesitant fuzzy minimal open and hesitant fuzzy maximal open sets in hesitant fuzzy topological space. Further, we investigate some properties with these new sets.