On proximity spaces and topological hyper nearrings

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:69 Issue:2
On proximity spaces and topological hyper nearrings

On proximity spaces and topological hyper nearrings

Authors : Somaye BORHANİNEJAD, B DAVVAZ

Pages : 1418-1427

Doi:10.31801/cfsuasmas.764635

View : 46 | Download : 11

Publication Date : 2020-12-31

Article Type : Research Paper

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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