# Digital topological groups

arXiv: https://arxiv.org/abs/2208.10748 · HTML: https://mlsanity.com/paper/2208.10748/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 19 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Builds on (most cited first, 1 of 1)

- [Digital homotopy relations and digital homology theories](https://mlsanity.com/paper/2106.01171/) (2021)

## Abstract (arXiv)

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 NP1- and NP2-digital topological groups, and investigate their properties and algebraic structure. The NP2 category is very restrictive, and we give a complete classification of NP2-digital topological groups. We also give many examples of NP1-digital topological groups. We define digital topological group homomorphisms, and describe the digital counterpart of the first isomorphism theorem.