Remarks on maximal open sets in m-spaces
Mohsen Rostamian Delavar
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
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.
Related papers
On Some Properties of Maximal M-Open Sets
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.
Some results on maximal open sets
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.
Some applications of M-open sets in topological 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.
New Note on Maximal E-Open and E-Semi- Maximal Open Sets in Topological Spaces
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.
Some Properties of µ-open Sets
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.
On the characterization of $M$-metrizable spaces
2017
We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM} and developed the idea further in \cite{AS}. In this paper we study locally $M$-metrizable spaces and the products of $M$-metrizable spaces. Finally we prove a characterization of commutatively metrizable topological spaces by means of the bases of a quasiuniformity.
γ-Operation in M-Topological Space
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.
Maximal perfect spaces
Bulletin of the Australian Mathematical Society, 1972
On Minimal Open Sets and Maps in Topological Spaces
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.
Some Properties of External E-Openand E-Closed Sets in Topological Spaces
International Journal for Research in Applied Science and Engineering Technology, 2017
In this work, some conditions for e-disconnectedness of a topological space in terms of maximal and minimal e-open sets and also some similarresults in terms of maximal and minimal e-closed sets along with interrelationships between themare investigated. Generally, we find that if a space has a setwhich is both maximal and minimal e-open, then either this set is the onlynontrivial e-open set in the space or the space is e-disconnected. We alsoobtain a result concerning a minimal e-open set on a subspace.
Related papers
New types of functions by M-open sets
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
On maximal μ-open and minimal μ-closed sets via generalized topology
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.
On some new maximal and minimal sets via semi-open
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 ...
More on Minimal δ-Open (Maximal δ-Closed) and δ-Semi-minimal Open (δ-Semi maximal Closed) Sets in 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.
More on -closed sets in topological spaces M as sobre conjuntos -cerrados en espacios topol ogicos
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.
On maximal, minimal and mean 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.
Further properties on M-continuity
Journal of the Egyptian Mathematical Society, 2013
The concept of M-open sets [1] can be applied in modifications of rough set approximations [2,3] which is widely applied in many application fields. The aim of this paper is to introduce and investigate some new classes of topological mappings called M-continuous mappings via M-open sets. Also, M-irresolute mappings which are stronger than M-continuous mappings are studied and the relationships between these mappings are investigated. Several properties of these new notions have been discussed and the connections between them are studied. (2000) MATHEMATICAL SUBJECT CLASSIFICATIONS: 54C08; 54D10; 54C05
On ωθ˜-µ-Open Sets in Generalized Topological Spaces
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.
On Minimal and Maximal Regular Open 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.
On maximal, minimal $\mu$-open and $\mu$-closed sets
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.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.