Abstract
Existence of an invariant metric on a topological group with a sequential topology was proved by Birkhoff [1] and Kakutani [2] independently. In the sequel we consider generally invariant metrics on a uniform space with a transformation group.
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Bibliography
Birkhorr, G.: A note on topological groups. Compositio Math. 3, 427–430 (1936).
Kakutani, S.: Über die Metrization der topologischen Gruppe. Proc. imp. Acad. Japan 12, 82–84 (1936).
Nakano, H.: Topology and linear topological spaces. Tokyo 1951.
Nakano, H.: Uniform spaces and transformation groups. It will be published in U.S.A.
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Dedicated to Professor Gottfried Köthe for the 60th birthday on December 25, 1965
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© 1966 Springer-Verlag Berlin Heidelberg
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Nakano, H. (1966). Invariant Metrics. In: Contributions to Functional Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85997-7_3
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DOI: https://doi.org/10.1007/978-3-642-85997-7_3
Publisher Name: Springer, Berlin, Heidelberg
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