Nonstandard hulls of locally uniform groups

Isaac Goldbring

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arXiv · 1203.6593

Nonstandard hulls of locally uniform groups

Isaac Goldbring

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Abstract

We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg'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.

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BibTeX RIS

Isaac Goldbring. 2012-03-29. Nonstandard hulls of locally uniform groups. https://arxiv.org/abs/1203.6593

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