Comparing the Floyd and ideal boundaries of a metric space
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- by Stephen M. Buckley and Simon L. Kokkendorff PDF
- Trans. Amer. Math. Soc. 361 (2009), 715-734 Request permission
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.References
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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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 715-734
- MSC (2000): Primary 54D35; Secondary 30F45, 53A30
- DOI: https://doi.org/10.1090/S0002-9947-08-04580-7
- MathSciNet review: 2452822