Advances in Pure Mathematics

Volume 8, Issue 5 (May 2018)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

Google-based Impact Factor: 0.50  Citations  h5-index & Ranking

The Unitary Group in Its Strong Topology

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DOI: 10.4236/apm.2018.85029    965 Downloads   1,757 Views  Citations


The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.

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Schottenloher, M. (2018) The Unitary Group in Its Strong Topology. Advances in Pure Mathematics, 8, 508-515. doi: 10.4236/apm.2018.85029.

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