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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2020 / Volume: 69 Issue: 2

On proximity spaces and topological hyper nearrings

Somaye Borhani-nejad(Yazd University)
B. Davvaz(Yazd University)0000-0003-1941-5372
Pages
—
Publication Date
2020-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In the following, we prove that every topological hyper nearring can be a proximity space.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In 1934 the concept of algebraic hyperstructures was first introduced by a French mathematician, Marty.
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Key Findings & Data: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.
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Conclusion & Impact:In the following, we prove that every topological hyper nearring can be a proximity space.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Heper nearring · Topological hyper nearrings · Complete part

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.

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Cite This Article

Borhani-nejad, S., Davvaz, B. (2020). On proximity spaces and topological hyper nearrings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 2. https://doi.org/10.31801/cfsuasmas.764635

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