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2020, IAEME Publication
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In this paper a new class of minimal open and minimal closed sets in topological spaces, namely minimal-open and minimal-closed sets are introduced. We give some basic properties and various characterizations of minimal-open and minimalclosed sets.
In this paper, we introduce and define minimal-open sets in topological spaces and we obtain some basic properties of this set. Moreover, we define-locally finite space and give some applications for finite minimal-open sets.
In this paper a new class of topological spaces called T min spaces and T max spaces and study their relations with topological spaces. Also a new class of maps called minimal continuous, maximal continuous, minimal irresolute, maximal irresolute, minimalmaximal continuous and maximal-minimal continuous maps in topological spaces and study their relations with various types of continuous maps. 2000 MATHEMATICS CLASSIFICATION: 54C05 Key words and phrases: Minimal open sets and Maximal open sets.
International Journal of Mathematics Trends and Technology, 2017
In 2008, Caldas M, Jafari S. and Noiri T. [7] introduced the concept of maximal -open sets, minimal -closed sets, -semi-maximal open and semi-minimal closed sets in general topological settings. In the present paper a new class of sets called minimal -open sets and maximal -closed sets in a topological space are introduced which are the -open sets and -closed sets respectively. The complement of minimal -open set is a maximal closed set. Some properties of -semi maximal closed sets, -semi minimal open sets are studied. Keywords-Minimal -open set, Maximal -closed set, -semi-minimal open set, -semi-maximal closed set.
International Mathematical Forum, 2009
In this article different forms of closed sets in m-spaces are introduced, studied and characterized. We show that the obtained results are a generalization of many of the results obtained by N. Rajesh in [10] and N. Rajesh et al. in [11].
Mathematics and Statistics, 2017
The purpose of this paper is to investigate the concepts of minimal and maximal regular open sets and their relations with minimal and maximal open sets. We study several properties of such concepts in a semi-regular space. It is mainly shown that if X is a semi-regular space, then m i O(X) = m i RO(X). We introduce and study new type of sets called minimal regular generalized closed. A special interest type of topological space called rT min space is studied and obtain some of its basic properties.
2017
Nakaoka and Oda ([1] and [2]) initiated the notion of maximal open (resp. minimal closed) sets in topological spaces. 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 -closed sets, -semi maximal open sets and -semi minimal closed sets and investigate some of their fundamental properties with example and counter examples.
2003
An �-space is a topological space in which the topology is generated by the family of all �-sets (see (N)). In this paper, minimal-�P-spaces (whereP denotes several separation axioms) are investigated. Some new characterizations of �-spaces are also obtained.
Journal of Al-Nahrain University Science, 2017
The present paper deals and discusses new types of sets all of these concepts completely depended on the concept of Beta open set. The importance concepts which introduced in this paper are minimal -open and maximal -open sets. Besides, new types of topological spaces introduced which called min T and max T spaces. Also we present new two maps of continuity which called minimal -continuous and maximal -continuous. Additionally we investigated some fundamental properties of the concepts which presented in this paper.
Demonstratio Mathematica, 2014
We characterize minimal Pγ-open sets in topological spaces. We show that any nonempty subset of a minimal Pγ-open set is pre Pγ-open. As an application of a theory of minimal Pγ-open sets, we obtain a sufficient condition for a Pγ-locally finite space to be a pre Pγ-Hausdorff space.
The American Mathematical Monthly, 1969
We introduce the notion of minimal open sets in a generalized topological space (X, µ). We investigate some of their fundamental properties and proved that any subset of a minimal open set on a GTS (X, µ) is a µ-preopen set.
Afrika Matematika, 2018
We see that the real numbers system with the usual topology contains no minimal open sets. This observation instigates us to study topological spaces having no minimal and maximal open sets. We find that such topological spaces if connected are not cut-point spaces. We also characterize mean open sets in T 1 connected topological spaces.
Annals of Pure and Applied Mathematics, 2020
In this paper, we present some important concepts indouble minimal space and study of (interior, closure) sets this space. Moreover, we give concepts ݎ݈ܽݑܴ݃݁ − ै ୈ −(open, closed) sets, a ै ୈ-(ࣛ, १, ी, ज़ ܽ݊݀ ࣝ) sets and find the relationship between these concepts.
Proyecciones (Antofagasta), 2020
In this paper, some new separation axioms called minimal normal, minimal c-normal and minimal compact spaces are introduce and investigate. Some of their basic properties in topological spaces are studied. Also their relationship among themselves as well as with other known separation axioms have been studied.
Proceedings of International Mathematical Sciences, 2022
In this article we have established the concept of multi-continuity in minimal structure spaces (in short M space) and the notion of product minimal space in Multiset topological space. Continuity between M-space, generalized Multiset topology and Multiset ideal topological spaces. We have investigated some basic properties of M-continuity in Multiset topological space, such as composition of M-continuous functions, product of M-continuous functions in product Multiset topological space etc.
viXra, 2020
The purpose of this paper is to introduce and characterize the concept of α-open set and several related notions in ideal minimal spaces.
Malaya Journal of Matematik, 2020
In this paper, we introduce and study cleanly µ-covered spaces along with two strong separation axioms in generalized topological spaces. Strong separation axioms are investigated by means of minimal µ-open and µ-closed sets of generalized topological spaces. Keywords µ-open set, µ-closed set, maximal µ-open set, minimal µ-open set, cleanly µ-covered.
The notion of maximal and minimal open sets in a topological space was introduced by [4] and [5]. In this paper, we introduce new classes of sets called maximal semi-open sets and minimal semi-open sets and investigate some of their fundamental properties. 2000 Mathematics Subject Classification: Primary: 54A05, 54A10; Secondary: 54E55. A.B.Khalaf and H.M.Hasan -On Some New Maximal and Minimal ...
Acta Mathematica Hungarica, 2012
We introduce the notion of maximal μ-open and minimal μclosed sets in a generalized topological space. We also investigate some of their fundamental properties.
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