ON PROXIMITY SPACES AND TOPOLOGICAL HYPER NEARRINGS
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.69, no.2, pp.1418-1427, 2020 (ESCI, TRDizin)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.