ON PROXIMITY SPACES AND TOPOLOGICAL HYPER NEARRINGS

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Borhani-Nejad S., Davvaz B.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.69, no.2, pp.1418-1427, 2020 (ESCI)

• Publication Type: Article / Article
• Volume: 69 Issue: 2
• Publication Date: 2020
• Doi Number: 10.31801/cfsuasmas.764635
• Journal Name: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
• Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Page Numbers: pp.1418-1427
• Keywords: Hyper nearring, topological hyper nearring, complete part, proximity relation, HYPERGROUPS
• Ankara Haci Bayram Veli University Affiliated: No

Abstract

In 1934 the concept of algebraic hyperstructures was.rst 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.