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Nonstandard hulls of locally uniform groups

Volume 220 / 2013

Isaac Goldbring Fundamenta Mathematicae 220 (2013), 93-118 MSC: Primary 22E65; Secondary 03H05. DOI: 10.4064/fm220-2-1

Abstract

We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxemburg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used to construct the hull. We use the nonstandard hull construction to give a nonstandard characterization of Enflo's notion of groups that are uniformly free from small subgroups. We prove that our nonstandard hull is locally isomorphic to Pestov's nonstandard hull for Banach–Lie groups. We also give some examples of infinite-dimensional Lie groups that are locally uniform.

Authors

  • Isaac GoldbringDepartment of Mathematics, Statistics, and Computer Science
    University of Illinois at Chicago
    Science and Engineering Offices (M/C 249)
    851 S. Morgan St.
    Chicago, IL 60607-7045, U.S.A.
    e-mail

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