2016/02/04 by Amrita Acharyya, Acharyya, Amrita, Jon M. Corson +3
Mathematics · #05C63 #20E18 #54F65 #57M15 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #math.GN #msc:05C63 #msc:20E18 #msc:54F65 #msc:57M15
paper · pdf · doi:10.48550/arxiv.1602.01782
arxiv created 2016/02/04 · openalex publication_date 2016/02/04 · arxiv updated 2016/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We have defined and established a theory of cofinite connectedness of a cofinite graph. Many of the properties of connectedness of topological spaces have analogs for cofinite connectedness. We have seen that if G is a cofinite group and Gamma=Gamma(G,X) is the Cayley graph. Then Gamma can be given a suitable cofinite uniform topological structure so that X generates G, topologically iff Gamma is cofinitely connected. Our immediate next concern is developing group actions on cofinite graphs. Defining the action of an abstract group over a cofinite graph in the most natural way we are able to characterize a unique way of uniformizing an abstract group with a cofinite structure, obtained from the cofinite structure of the graph in the underlying action, so that the aforesaid action becomes uniformly continuous.