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2015
In this paper we extend the notions of γ-operation, pre-open msets , αopen msets, semi open msets, b-open msets and β-open msets to M-topological spaces. These types of msets are new classes of multisets. We study the relations between these different types of submsets of M-topological spaces. Also, we study some of their properties and show that these types generalize the notion of open (closed) msets.
The aim of this paper is to introduce and investigate some new classes of mappings called contra-M-continuous mappings and almost contra-M-continuous mappings via M-open sets. Also, the relationships between these mappings and other types are discussed. Several properties of these new notions are investigated and the connections between them are studied.
Cubo (Temuco), 2018
In this paper, we introduced the notion of γ-semi-open sets and γ-P-semi-open sets in (a)topological spaces which is a set equipped with countable number of topologies. Several properties of these notions are discussed. RESUMEN En este artículo, introducimos la noción de conjuntos γ-semi-abiertos y conjuntos γ-Psemi-abiertos en espacios (a)topológicos, el cual es un conjunto dotado con una cantidad numerable de topologías. Discutimos diversas propiedades de estas nociones.
Scientiae Mathematicae Japonicae, 2008
In this paper, we present concepts of pre γp-open sets and pre γpclosures of a subset in a topological space, where γp is an operation on the family of all preopen sets of the topological space, and study some topological properties on them. As its application, we introduce the concept of pre γp-Ti spaces (i = 0, 1/2, 1, 2) and study some properties of these spaces.
Bol.Soc.Paran. Mat., 2017
In this paper, we introduce and study some properties of the new sets namely * ∧µ-sets, * ∨µ-sets, * λµ-closed sets, * λµ-open sets in a generalized topological space.
International Journal of Analysis and Applications
In this paper analogous to [1], we introduce a new class of sets called ωθ˜-µ-open sets in generalized topological spaces which lies strictly between the class of θ˜µ-open sets and the class of ω-µ-open sets. We prove that the collection of ωθ˜-µ-open sets forms a generalized topology. Finally, several characterizations and properties of this class have been given.
Malaya Journal of Matematik, 2018
In this paper, we study semi-open, pre-open, α-open and β-open sets, and obtain some relations between them.
Research Square (Research Square), 2023
Recently, El-Sharkasy et al., El-Sharkasy and Badr have shown that to find the mutations of deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), multiset topology is very much essential. In this article we give the definitions of mixed (1, 2)-pre-open (resp. mixed (1, 2)-semi-open, mixed (1, 2)-α-open, mixed (1, 2)β-open) mset via two multiset topologies. Besides, we procure the notions of mixed (1, 2)-pre (resp. mixed (1, 2)-semi, mixed (1, 2)α, mixed (1, 2)-β) mset continuity between two M-topological spaces (M, τ1), (M, τ2) and an M-topological space (N, σ). A decomposition of these types is investigated. Finally, we prove that every τ1-mset continuous function is mixed (1, 2)-pre-(resp. mixed (1, 2)semi-, mixed (1, 2)-α-, mixed (1, 2)-β-) mset continuous function.
The notion of semi-convergence of filters was introduced by the author in [Math. J. Okayama Univ. 41, 103–109 (1999; Zbl 0970.54003)] when investigating some characterizations related to semi-open continuous functions. W. K. Min [Int. J. Math. Math. Sci. 31, 177–181 (2002; Zbl 0993.54015)] used the idea of semi-convergence of filters to introduce a new class of sets, called γ-open sets, and the notions of γ-closure, γ-interior and γ-continuity and to investigate some properties. In this paper we continue to explore further properties of these notions as well as characterizations of γ-open sets. We also introduce and study topological properties of γ-derived, γ-border, γ-frontier, and γ-exterior of a set using the concept of γ-open sets.
International journal of computer applications, 2017
Nakaoka and Oda ([1] and [2]) initiated the notion of maximal open (resp. minimal closed) sets in topological spaces. Thereafter, in 2005, Cao,Ganster, Reilly and Steiner [4] introduced -open (resp. -closed) sets in general topology. In the present work, the author introduces new classes of open and closed sets called maximal -open sets, minimal -open sets, maximal -closed sets, minimal -closed sets, -semi maximal open and -semi minimal closed and investigate some of their fundamental properties. Keywords -open, -open, maximal (resp. minimal) -open, maximal (resp. minimal) -closed, -semi maximal open and semi minimal closed sets. Definition 2.1 [3]. Let A be a subset of a space X. A point xX is called a -cluster point of A if ACl(U) , for every open set U of X containing x. The set of all -cluster points of A is called the -closure of A, denoted by Cl (A). Definition 2.2 [3]. A subset A of X is called -closed if A = Cl (A). The complement of a -closed set is called -open set in X. We denote the collection of all -open (respectively, -closed) sets by -O(X,) (respectively, -C(X,)). Definition 2.3 [3]. Let A be a subset of a space X. A point xX is called a -cluster point of A if AU , for every regular open set U of X containing x. The set of all -cluster points of A is called the -closure of A, denoted by Cl (A). Definition 2.4 [3]. A subset A of X is called -closed if A = Cl (A). The complement of a -closed set is called -open set in X. We denote the collection of all -open (respectively, -closed) sets by -O(X,) (respectively, -C(X,)).
Acta Mathematica Hungarica, 2011
A new kind of sets called generalized μ-closed (briefly gμ-closed) sets are introduced and studied in a topological space by using the concept of generalized open sets introduced byÁ. Császár. The class of all gμ-closed sets is strictly larger than the class of all μ-closed sets. Furthermore, g-closed sets (in the sense of N. Levine ) is a special type of gμ-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of μg-regular and μg-normal spaces have been given.
Journal of Taibah University for Science, 2013
The aim of this paper is to introduce and study some new classes of mappings called M-open, M-closed, pre-M-open, pre-M-closed and super M-open by M-open sets. Also, the relationships between these mappings are discussed. Several properties of these types of mappings are presented. © 2013 Taibah University. Production and hosting by Elsevier B.V. All rights reserved. MSC: 54C05; 54C08; 54C10 Keywords: M-Open; Pre-M-open; Super M-open mappings; M-T1-Spaces; M-T2-Spaces; M-Compact; M-Connected spaces
2004
In the present paper, we introduce and study topological properties of µ-derived, µ-border, µ-frontier and µ-exterior of a set using the con- cept of µ-open sets and study also other properties of the well known notions of µ-closure and µ-interior.
Journal of the Egyptian Mathematical Society, 2014
In this paper, the notion of a-c-I-open sets in a topological space together with its corresponding interior and closure operators are introduced. Further, the concept of a-c-I-continuous functions and a-c-I-open functions are introduced and some of their basic properties are studied.
Boletim da Sociedade Paranaense de Matemática, 2017
In this paper, we introduce and study some properties of the new sets namely * Λµ- sets , * V µ- sets, * λµ- closed sets, * λµ- open sets in generalized topological space.
In this paper, we introduce the concept of an operation γ on a family of b-open sets in a topological space (X, τ). Using this operation γ, we introduce the concept of b-γ-open sets and study some of their properties.
2007
In this paper, we introduce and study topological properties of - derived, -border, -frontier and -exterior of a set using the concept of -open sets. We also present and study new separation axioms by using the notions of -open and -closure operator.
Mathematical Communications, 2011
In this paper, we introduce the concept of an operation γ on a family of β-open sets denoted by βO(X) in a topological space (X, τ). Using the operation γ on βO(X), we introduce the concept of β-γ-open sets, and investigate the related topological properties. We also introduce the notion of β-γ-T i spaces (i = 0, 1/2, 1, 2) and study some topological properties on them. Further, we introduce β-(γ, b)-continuous maps and investigate basic properties. Finally, we investigate a general operation approach to β-closed graphs of mappings.
Journal of Mathematical and Computational Science, 2021
Using the idea of µ-pre*-closed set in generalized topological space, the concept of µ-pre*-closure and µpre*-interior in generalized topological space have been studied and several of their properties are proved. In this paper we are introducing some new operators in µ-pre* closed sets in generalized topological space as µ-pre*dervied, µ-pre*-border, µ-pre*-frontier and µ-pre*-exterior. Also the aim is to deal with some basic properties.
The purpose of the present paper is to introduce and investigate two new classes of continuous multifunctions called upper/lower e-I-continuous multifunctions and upper/lower I -continuous multifunctions by using the concepts of e-I-open sets and I -open sets. The class of upper/lower e-I-continuous multifunctions is contained in that of upper/lower I -continuous multifunctions. Several characterizations and fundamental properties concerning upper/lower e-I-continuity and upper/lower I -continuity are obtained.
International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2023
In this paper, some characterizations and proportion of notion a investigated. Throughout this paper (X, τ) and (Y, σ) (simply, X and Y) represent topological spaces on which separation axioms are assumed unless otherwise mentioned. We introduce a new class of sets called regular generalized open sets which is properly placed in between the class of open sets and the class of-open sets. Throughout this paper (X, ) represents a topological space on which no separation axiom is assumed unless otherwise mentioned. For a subset A of a topological space X, cl (A) and int (A) denote the closure of A and the interior of A respectively. X/A or Ac denotes the complement of A in X. introduced and investigated semi open sets, generalized closed sets, regular semi open sets, weakly closed sets, semi generalized closed sets , weakly generalized closed sets, strongly generalized closed sets, generalized pre-regular closed sets, regular generalized closed sets, and generalized -generalized closed sets respectively.
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