57,446 research outputs found
Cofinite Graphs and their Profinite Completions
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
- …