Nonstandard hulls of locally uniform groups

Isaac Goldbring. "Nonstandard hulls of locally uniform groups." Fundamenta Mathematicae 220.2 (2013): 93-118. <http://eudml.org/doc/283243>.

@article{IsaacGoldbring2013,
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.},
author = {Isaac Goldbring},
journal = {Fundamenta Mathematicae},
keywords = {nonstandard hull; locally uniform group; functionality; convex vector space; Banach-Lie group},
language = {eng},
number = {2},
pages = {93-118},
title = {Nonstandard hulls of locally uniform groups},
url = {http://eudml.org/doc/283243},
volume = {220},
year = {2013},
}

TY - JOUR
AU - Isaac Goldbring
TI - Nonstandard hulls of locally uniform groups
JO - Fundamenta Mathematicae
PY - 2013
VL - 220
IS - 2
SP - 93
EP - 118
AB - 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.
LA - eng
KW - nonstandard hull; locally uniform group; functionality; convex vector space; Banach-Lie group
UR - http://eudml.org/doc/283243
ER -