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- Title
Cofinite Graphs and Groupoids and their Profinite Completions.
- Authors
ACHARYYA, AMRITA; CORSON, JON M.; DAS, BIKASH
- Abstract
Cofinite graphs and cofinite groupoids are defined in a unified way extending the notion of cofinite group introduced by Hartley. These objects have in common an underlying structure of a directed graph endowed with a certain type of uniform structure, called a cofinite uniformity. Much of the theory of cofinite directed graphs turns out to be completely analogous to that of cofinite groups. For instance, the completion of a directed graph Γ with respect to a cofinite uniformity is a profinite directed graph and the cofinite structures on Γ determine and distinguish all the profinite directed graphs that contain Γ as a dense sub-directed graph. The completion of the underlying directed graph of a cofinite graph or cofinite groupoid is observed to often admit a natural structure of a profinite graph or profinite groupoid, respectively.
- Subjects
GROUPOIDS; GROUP theory; GRAPH theory; DIRECTED graphs; PROFINITE groups; UNIFORM spaces
- Publication
Kyungpook Mathematical Journal, 2018, Vol 58, Issue 2, p399
- ISSN
1225-6951
- Publication type
Article
- DOI
10.5666/KMJ.2018.58.2.399