End compactifications in non-locally-finite graphs
摘要
There are different definitions of ends in non-locally-finite graphs which are all equivalent in the locally finite case. We prove the compactness of the end-topology that is based on the principle of removing finite sets of vertices and give a proof of the compactness of the end-topology that is constructed by the principle of removing finite sets of edges. For the latter case there exists already a proof in \cite{cartwright93martin}, which only works on graphs with countably infinite vertex sets and in contrast to which we do not use the Theorem of Tychonoff. We also construct a new topology of ends that arises from the principle of removing sets of vertices with finite diameter and give applications that underline the advantages of this new definition.
引用
@article{arxiv.math/0010033,
title = {End compactifications in non-locally-finite graphs},
author = {B. Krön},
journal= {arXiv preprint arXiv:math/0010033},
year = {2009}
}
备注
17 pages, to appear in Math. Proc. Cambridge Philos. Soc