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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Comparing the Floyd and ideal boundaries of a metric space


Authors: Stephen M. Buckley and Simon L. Kokkendorff
Journal: Trans. Amer. Math. Soc. 361 (2009), 715-734
MSC (2000): Primary 54D35; Secondary 30F45, 53A30
Published electronically: September 29, 2008
MathSciNet review: 2452822
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Abstract: We discuss and compare the notions of ideal boundaries, Floyd boundaries and Gromov boundaries of metric spaces. The three types of boundaries at infinity are compared in the general setting of unbounded length spaces as well as in the special cases of CAT(0) and Gromov hyperbolic spaces. Gromov boundaries, usually defined only for Gromov hyperbolic spaces, are extended to arbitrary metric spaces.


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Additional Information

Stephen M. Buckley
Affiliation: Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, Ireland
Email: Stephen.Buckley@may.ie

Simon L. Kokkendorff
Affiliation: Department of Mathematics, Technical University of Denmark, Building 303, 2800 Kgs. Lyngby, Denmark
Address at time of publication: National Survey and Cadastre, Rentemestervej 8, 2400 Copenhagen, Denmark
Email: s.l.kokkendorff@mat.dtu.dk, simlk@kms.dk

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04580-7
PII: S 0002-9947(08)04580-7
Keywords: Ideal boundary, Floyd boundary, conformal distortion, Gromov hyperbolicity, Gromov boundary, CAT(0)-spaces
Received by editor(s): January 15, 2006
Received by editor(s) in revised form: November 3, 2006
Published electronically: September 29, 2008
Additional Notes: The first author was partially supported, and the second author fully supported, by Enterprise Ireland
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.