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On the Continuity of the Evaluation Mapping Associated with a Group and Its Character Group
Proceedings of the American Mathematical Society
Vol. 126, No. 11 (Nov., 1998), pp. 3413-3415
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/119163
Page Count: 3
You can always find the topics here!Topics: Topological compactness, Mathematical duality, Personnel evaluation, Isomorphism, Homomorphisms, Topology, Topological theorems, Mathematical theorems, Topological vector spaces
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For an abelian Hausdorff group G, let G* denote the character group endowed with the compact-open topology and let α G: G → G* * denote the canonical homomorphism. We show that the evaluation mapping from G*× G into the torus is continuous if and only if G* is locally compact and α G is continuous. If α G is injective and open, then the evaluation mapping is continuous if and only if G is locally compact. Several examples and counterexamples are given.
Proceedings of the American Mathematical Society © 1998 American Mathematical Society