On Schwartz groups
Volume 181 / 2007
Studia Mathematica 181 (2007), 199-210
MSC: 22A05, 46A11.
DOI: 10.4064/sm181-3-1
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.
