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On Schwartz groups

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Außenhofer L., Chasco M., Domínguez X., Tarieladze V.

Studia Mathematica

2007

tom 181

nr 3

199-210

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.

Ograniczanie wyników

1 Studia Mathematica

1 Außenhofer L.

1 Chasco M.

1 Domínguez X.

1 Tarieladze V.

1 2007

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On Schwartz groups