Cofinite Connectedness and Cofinite Group Actions
Abstract
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 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 generates , 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.
Cite
@article{arxiv.1602.01782,
title = {Cofinite Connectedness and Cofinite Group Actions},
author = {Amrita Acharyya and Jon M. Corson and Bikash Das},
journal= {arXiv preprint arXiv:1602.01782},
year = {2016}
}