Abstract
In 1934 the concept of algebraic hyperstructures was first introduced by a French mathematician, Marty. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the result of this composition is a set. In this paper, we prove some results in topological hyper nearring. Then we present a proximity relation on an arbitrary hyper nearring and show that every hyper nearring with a topology that is induced by this proximity is a topological hyper nearring. In the following, we prove that every topological hyper nearring can be a proximity space.
Highlights
In 1934, the concept of hypergroups was ...rst introduced by a French mathematician, Marty [22]
We present a proximity relation on an arbitrary hyper nearring and show that every hyper nearring with a topology that is induced by this proximity is a topological hyper nearring
We show that every topological hyper nearring is a proximity space
Summary
In 1934, the concept of hypergroups was ...rst introduced by a French mathematician, Marty [22] In the following, it was studied and extended by many researchers, namely, Corsini [3], Corsini and Leoreanu [4], Davvaz [6,7,8], Frenni [12], Koskas [20], Mittas [23], Vougiouklis, and others. In the 1950’s, Efremovi1⁄4c [10, 11], a Russian mathematician, gave the de...nition of proximity space, which he called in...nitesimal space in a series of his papers. He axiomatically characterized the proximity relation A is near B for subsets A and B of any set X. We show that every topological hyper nearring is a proximity space
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call