Nonstandard hulls of locally uniform groups

• Autorzy: Isaac Goldbring
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03H05: Nonstandard models in mathematics
• 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 220
• Numer: 2
• Strony: 93-118

Daty

wydano

2013

Twórcy

autor

Isaac Goldbring

• Department 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.

Identyfikatory

DOI

10.4064/fm220-2-1