Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T01:02:44.687Z Has data issue: false hasContentIssue false
  • English
  • Français

End compactifications in non-locally-finite graphs

Published online by Cambridge University Press:  26 November 2001

B. KRÖN
B. KRÖN
Affiliation:
Current address: Institut für Mathematik C, Technische Universität Graz, Steyrergasse 30, 8010 - Graz, tel.: +43/316/873-4509, e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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 [1], 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 3 , November 2001 , pp. 427 - 443
Copyright
© 2001 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)