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Lee, Dae-Woong; Staecker, P. Christopher

Digital topological groups. (English) Zbl 1542.22004

Topology Appl. 338, Article ID 108644, 20 p. (2023).
Summary: In this article, we develop the basic theory of digital topological groups. The basic definitions directly lead to two separate types, based on the details of the continuity required of the group multiplication. We define NP\({}_1\)- and NP\({}_2\)-digital topological groups, and investigate their properties and algebraic structure. The NP\({}_2\)-type is very restrictive, and we give a complete classification of NP\({}_2\)-digital topological groups. We also give many examples of NP\({}_1\)-digital topological groups. We define digital topological group homomorphisms, and describe the digital counterpart of the first isomorphism theorem.

Cited in 1 Document

MSC:

22A30 Other topological algebraic systems and their representations
22A10 Analysis on general topological groups
68U03 Computational aspects of digital topology
05C10 Planar graphs; geometric and topological aspects of graph theory
54H11 Topological groups (topological aspects)
54H30 Applications of general topology to computer science (e.g., digital topology, image processing)

Keywords:

digital image; normal product adjacency; NP\({}_i\)-digital topological group; digital simple closed curve; regular graph; vertex-transitive graph; Cayley graph; digital topological group homomorphism; digital open map; digital H-space
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