On proximity spaces and topological hyper nearrings

Year 2020, Volume: 69 Issue: 2, 1418 - 1427, 31.12.2020

Somaye Borhani-nejad B. Davvaz

https://doi.org/10.31801/cfsuasmas.764635

Cited By: 1

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.

Keywords

Heper nearring, Topological hyper nearrings, Complete part, Proximity relation

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