Vol. 4, No. 2, 2011

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 2, 181–360
Issue 1, 1–180

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
Other MSP Journals
The visual boundary of $\mathbb{Z}^2$

Kyle Kitzmiller and Matt Rathbun

Vol. 4 (2011), No. 2, 103–116

We introduce ideas from geometric group theory related to boundaries of groups. We consider the visual boundary of a free abelian group, and show that it is an uncountable set with the trivial topology.

boundary, visual boundary, Cayley graph, $\mathbb Z^2$, geodesic ray, quasi-isometry
Mathematical Subject Classification 2000
Primary: 20F05, 20F69, 51F99
Received: 28 April 2009
Revised: 6 March 2011
Accepted: 7 March 2011
Published: 17 January 2012

Communicated by Kenneth S. Berenhaut
Kyle Kitzmiller
Department of Mechanical Engineering
San Diego State University
5500 Campanile Drive
San Diego, CA 92182-1323
United States
Matt Rathbun
Department of Mathematics
University of California
One Shields Ave.
Davis, CA 95616
United States
Department of Mathematics
Huxley Building 6M33
Imperial College London, South Kensington Campus
London, SW7 2AZ
United Kingdom