Ultralimits of Metric Spaces

  • Michael Kapovich
Part of the Modern Birkhäuser Classics book series (MBC)


Let (Xi) be a sequence of metric spaces. One can describe the limiting behavior of the sequence (X i ) by studying limits of sequences of finites subsets Y i X i . Ultrafilters are an efficient techn ical device for simultaneously taking limits of all such sequences of subspaces and putting them tgether to form one object, namely, an ultralimit of (X i ) (see [KL95, KL97, KKL98, Dru00] for examples of application of ultralimits to the study of quasiisometries of metric spaces). We discuss the concept of ultralimits folllowing [Gro93] and [KL95].


Hausdorff Distance Geodesic Segment Continuous Embedding Asymptotic Cone Geodesic Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, DavisDavisU.S.A.

Personalised recommendations