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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-2-1,
author = {Isaac Goldbring},
title = {Nonstandard hulls of locally uniform groups},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {93-118},
zbl = {1272.22008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-2-1}
}
Isaac Goldbring. Nonstandard hulls of locally uniform groups. Fundamenta Mathematicae, Tome 220 (2013) pp. 93-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-2-1/