Abstract
The purpose of this paper is to introduce the notions of m-asymmetric semiopen sets and M-asymmetric semicontinuous multifunctions defined between asymmetric sets satisfying certain minimal conditions in the framework of bitopological spaces. Some new characterizations of m-asymmetric semiopen sets and M-asymmetric semicontinuous multifunctions will be investigated and several fundamental properties will be obtained.
Highlights
The concept of topology is an important tool that has received considerable attention from many scholars in many fields of applied sciences and other branches of pure mathematics
In 2000, Popa and Noiri [9], introduced and studied the concepts of m-structures and M-continuous function as a function defined between topologies satisfying certain minimal conditions
We introduce and investigate some basic characterizations and properties of m-asymmetric semiopen sets, m-asymmetric semiclosed sets and, upper and lower M-asymmetric semicontinuous multifunctions in the realm of bitopological spaces satisfying a minimal structure, which is a generalization of results of Noiri and Popa [10] and Berge [5]
Summary
The concept of topology is an important tool that has received considerable attention from many scholars in many fields of applied sciences and other branches of pure mathematics. In 2000, Popa and Noiri [9], introduced and studied the concepts of m-structures and M-continuous function as a function defined between topologies satisfying certain minimal conditions They showed that the M-continuous functions have properties similar to those of continuous functions between topological spaces. With these ideas of multifunction continuity and M-continuous functions, Noiri and Popa [10] introduced and studied upper and lower M-continuous multifunctions and showed how these functions have properties similar to those of upper and lower continuous functions and continuous multifunctions between topological spaces In this present paper, we introduce and investigate some basic characterizations and properties of m-asymmetric semiopen sets, m-asymmetric semiclosed sets and, upper and lower M-asymmetric semicontinuous multifunctions in the realm of bitopological spaces satisfying a minimal structure, which is a generalization of results of Noiri and Popa [10] and Berge [5].
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