Cofinite graphs and their profinite completions

Amrita Acharyya, Jon M Corson, Bikash Das


We generalize the idea of cofinite groups, due to B. Hartley, [2]. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions.

The idea of constructing a cofinite graph starts with defining a uniform topological graph $\Gamma$, in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over $\Gamma$. It is established that for any cofinite graph there exists a unique cofinite completion.


profinite graph, cofinite graph, profinite group, cofinite group, uniform space, completion, cofinite entourage

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ISSN: 2338-2287

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