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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.
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.
IAEME Publication, 2020
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.
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.
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.
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.
The American Mathematical Monthly, 1969
International Mathematical Forum
In this paper, we introduce a new class of open sets in a topological space called − open sets. We study some properties and several characterizations of this class, also we explain the relation of − open sets with many other classes of open sets. Furthermore, we define − closed sets and − closed sets and we give some fundamental properties and relations between these classes and other classes such as − closed and − closed sets.
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.
Proyecciones (Antofagasta), 2020
International Journal of Mathematics Trends and Technology, 2017
E. Ekici [8] introduced e-open (resp. eclosed) sets in general topology. Thereafter Nakaoka and Oda ([1] and [2]) initiated the notion of maximal open (resp. minimal closed) sets in topological spaces. In the present work, the author introduces new classes of open and closed sets called maximal e-open sets, minimal e-closed sets, esemi maximal open and e-semi minimal closed and investigate some of their fundamental properties with example and counter examples.
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 ...
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.
Journal of Al-Nahrain University Science, 2011
In this work we introduce maximal m-open set in minimal structure spaces and study some of their basic properties in these spaces.
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.
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.
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].
Kirkuk University Journal-Scientific Studies, 2007
The aim of this paper is to introduce and study some properties of pre--open sets,and study a new class of spaces, called p-regular space. Determine some properties of p-regularity and compare with other types of regular spaces.
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.
Applied General Topology, 2013
In this paper, a new class of sets called µ-generalized closed (briefly µg-closed) sets in generalized topological spaces are introduced and studied. The class of all µg-closed sets is strictly larger than the class of all µ-closed sets (in the sense ofÁ. Császár). Furthermore, g-closed sets (in the sense of N. Levine) is a special type of µg-closed sets in a topological space. Some of their properties are investigated here. Finally, some characterizations of µ-regular and µ-normal spaces have been given.
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