On Schwartz groups

L. Außenhofer, et al. "On Schwartz groups." Studia Mathematica 181.3 (2007): 199-210. <http://eudml.org/doc/285252>.

@article{L2007,
abstract = {We introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topological vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over hemicompact k-spaces are Schwartz groups. We also prove that every hemicompact k-space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group.},
author = {L. Außenhofer, M. J. Chasco, X. Domínguez, V. Tarieladze},
journal = {Studia Mathematica},
keywords = {Schwartz vector space; Schwartz group; nuclear group; hemicompact space},
language = {eng},
number = {3},
pages = {199-210},
title = {On Schwartz groups},
url = {http://eudml.org/doc/285252},
volume = {181},
year = {2007},
}

TY - JOUR
AU - L. Außenhofer
AU - M. J. Chasco
AU - X. Domínguez
AU - V. Tarieladze
TI - On Schwartz groups
JO - Studia Mathematica
PY - 2007
VL - 181
IS - 3
SP - 199
EP - 210
AB - We introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topological vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over hemicompact k-spaces are Schwartz groups. We also prove that every hemicompact k-space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group.
LA - eng
KW - Schwartz vector space; Schwartz group; nuclear group; hemicompact space
UR - http://eudml.org/doc/285252
ER -