Digital topological groups

08/23/2022

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by   Dae-Woong Lee, et al.

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CHONBUK NATIONAL UNIVERSITY

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Fairfield University

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In this article, we develop the basic theory of digital topological groups. The basic definitions directly lead to two separate categories, based on the details of the continuity required of the group multiplication. We define _1- and _2-digital topological groups, and investigate their properties and algebraic structure. The _2 category is very restrictive, and we give a complete classification of _2-digital topological groups. We also give many examples of _1-digital topological groups. We define digital topological group homomorphisms, and describe the digital counterpart of the first isomorphism theorem.