Some Properties of µ-open Sets

2004

In the present paper, we introduce and study topological properties of θ-derived, θ-border, θ-frontier and θ-exterior of a set using the concept of θ-open sets and study also other properties of the well known notions of θ-closure and θ-interior.

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.

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.

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.

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.

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 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.

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 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.

Divulgaciones Matematicas

In the present paper, we introduce and study topological properties of θ-derived, θ-border, θ-frontier and θ-exterior of a set using the concept of θ-open sets and study also other properties of the well known notions of θ-closure and θ-interior. Key words and phrases: θ-open, θ-closure, θ-interior, θ-border, θfrontier, θ-exterior.