• Communications of the Korean Mathematical Society
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• v.30 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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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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• v.39 no.3_4
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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.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1259-1265
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• 2016

In this paper, we introduce the notions of mean open and closed sets in topological spaces, and obtain some properties of such sets. We observe that proper paraopen and paraclosed sets are identical to mean open and closed sets respectively.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.103-113
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• 2022

The notions of soft rough pre open set, soft rough pre closed set, soft rough dense set, soft rough sub maximal, soft rough pre interior and soft rough pre closure are introduced and studied. We also investigate some related properties of these concepts.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.743-749
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• 2021

The purpose of this article is to study few properties of fuzzy mean open and fuzzy mean closed sets in fuzzy topological spaces. Further, the idea of fuzzy mean clopen set is introduced. It is observed that a fuzzy mean clopen set is both fuzzy mean open and fuzzy mean closed but the converse is not true.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.53-67
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• 2019

The notions of closed elements and dense elements are introduced in BE-algebras. Characterization theorems of closed elements and closed filters are obtained. The notion of dense elements is introduced in BE-algebras. Dense BE-algebras are characterized with the help of maximal filters and congruences. The concept of D-filters is introduced in BE-algebras. A set of equivalent conditions is derived for every D-filter to become a closed filter.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.11-19
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• 2023

Let 𝓗₀ be the set of rings R such that Nil(R) = Z(R) is a divided prime ideal of R. The concept of maximal non φ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in 𝓗₀. This generalization was introduced in [20] where the authors proved that if R ∈ 𝓗₀ is an integrally closed ring with finite Krull dimension, then R is a maximal non φ-chained subring of T(R) if and only if R is not local and |[R, T(R)]| = dim(R) + 3. This motivates us to investigate the other natural numbers n for which R is a maximal non φ-chained subring of some overring S. The existence of such an overring S of R is shown for 3 ≤ n ≤ 6, and no such overring exists for n = 7.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.185-191
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• 2012

Let D be an integral domain and SF(D) be the set of star operations of finite type on D. We show that if ${\mid}SF(D){\mid}$ < ${\infty}$, then every maximal ideal of D is a $t$-ideal. We give an example of integrally closed quasi-local domains D in which the maximal ideal is divisorial (so a $t$-ideal) but ${\mid}SF(D){\mid}={\infty}$. We also study the integrally closed domains D with ${\mid}SF(D){\mid}{\leq}2$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.643-653
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• 2012

Let $f\;:\;M\;{\rightarrow}\;M$ be a diffeomorphism on a closed $C^{\infty}$ manifold. Let $\Lambda$ be a transitive set. In this paper, we show that (i) $C^1$-generically, $f$ has the shadowing property on a locally maximal $\Lambda$ if and only if $\Lambda$ is hyperbolic, (ii) f has the $C^1$-stably shadowing property on $\Lambda$ if and only if $\Lambda$ is hyperbolic.