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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-3-1,
author = {L. Au\ss enhofer and M. J. Chasco and X. Dom\'\i nguez and V. Tarieladze},
title = {On Schwartz groups},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {199-210},
zbl = {1126.22001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-3-1}
}
L. Außenhofer; M. J. Chasco; X. Domínguez; V. Tarieladze. On Schwartz groups. Studia Mathematica, Tome 178 (2007) pp. 199-210. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-3-1/