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Galois connections and isomorphism of simultaneous ordered relations

School of Mathematical Sciences, Moolji Jaitha College Jalgaon-425001, India

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Annals of Communications in Mathematics 2023
, 6 (2),
109-117.
https://doi.org/10.62072/acm.2023.060204
Received: 11 Apr 2023 |
Accepted: 25 May 2023 |
Published: 30 Jun 2023

Abstract

In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper we have presented how partially ordered sets can be studied under simultaneous partially ordered relations which we have called binary posets. The paper is motivated by the problem of operating a set simultaneously under two distinct partially ordered relations. It has been shown that binary posets follow duality principle just like posets do. Within this framework, some new definitions concerning maximal and minimal elements are also presented. Furthermore, some theorems on order isomorphism and Galois connections are derived.

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Cite This Article

Galois connections and isomorphism of simultaneous ordered relations.

Annals of Communications in Mathematics,

2023,
6 (2):
109-117.
https://doi.org/10.62072/acm.2023.060204
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  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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