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2011, Journal of Al-Nahrain University Science
In this work we introduce maximal m-open set in minimal structure spaces and study some of their basic properties in these spaces.
This paper deals with maximal m-open sets. The m-closure and the m-interior of maximal m-open sets and their properties are investigated. Further, the behaviors of maximal m-open sets in m-homeomorphic m-spaces and product m-spaces are inspected. Our results are supported by some examples and counterexamples.
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].
2012
In this paper, the notion of maximal m-open set is introduced and its properties are investigated. Some results about existence of maximal m-open sets are given. Moreover, the relations between maximal m-open sets in an m-space and maximal open sets in the corresponding generated topology are considered. Our results are supported by examples and counterexamples.
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.
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.
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.
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.
Chaos, Solitons & Fractals, 2009
In this paper, minimal Euclidean space and minimal upper and lower semicontinuous functions are introduced and some properties of them are considered. It is shown that every m-continuous function from ðX ; MÞ to M 1 attains its maximum and minimum values, if ðX ; MÞ is an m-compact space.
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.
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.
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.
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.
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.
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.
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.
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.
Acta Universitatis Sapientiae, Mathematica
The intention of this article is to introduce and characterise the concept of preopen sets and prelocally closed sets in Generalised Topology and Minimal structure spaces.
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.
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