Ultralimits of Metric Spaces
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].
KeywordsHausdorff Distance Geodesic Segment Continuous Embedding Asymptotic Cone Geodesic Space
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