Cofinite Graphs and their Profinite Completions

2016/02/04 by Amrita Acharyya, Acharyya, Amrita, Jon M. Corson +3
Mathematics · #05C63 #20E18 #54F65 #57M15 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:05C63 #msc:20E18 #msc:54F65 #msc:57M15

paper · pdf · doi:10.48550/arxiv.1602.01866

arxiv created 2016/02/04 · arxiv updated 2016/02/08

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.

Related

• Cofinite Graphs and Groupoids and their Profinite Completions
• Cofinite Connectedness and Cofinite Group Actions
• The profinite completion of the fundamental group of infinite graphs of groups
• Uniform hyperfiniteness
• Research problem: The completion number of a graph