Cofinite Graphs and their Profinite Completions
General Topology
2016-02-08 v1
Abstract
We generalize the idea of cofinite groups, due to B. Hartley. 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.
Cite
@article{arxiv.1602.01866,
title = {Cofinite Graphs and their Profinite Completions},
author = {Amrita Acharyya and Jon M. Corson and Bikash Das},
journal= {arXiv preprint arXiv:1602.01866},
year = {2016}
}