2014/04/01 by Johannes Carmesin, Carmesin, Johannes
Mathematics · #Advanced Topology and Set Theory #math.CO #msc:05C63
paper · pdf · doi:10.48550/arxiv.1404.0151
arxiv created 2014/04/01 · arxiv updated 2014/04/02
Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid. As our main tool, we prove for any infinite graph G with vertex sets A and B that if every finite subset of A is linked to B by disjoint paths, then the whole of A can be linked to the closure of B by disjoint paths or rays in a natural topology on G and its ends. This latter theorem re-proves and strengthens the infinite Menger theorem of Aharoni and Berger for `well-separated' sets A and B. It also implies the topological Menger theorem of Diestel for locally finite graphs.