locally compact group

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English[edit]

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Noun[edit]

locally compact group (plural locally compact groups)

  1. (topology) A topological group whose underlying topology is both locally compact and Hausdorff.
    • 1988, J. M. G. Fell, R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Volume 1, Academic Press, page 63:
      Indeed, if there is one property of locally compact groups more responsible than any other for the rich positive content of their representation theory, it is their possession of left-invariant and right-invariant (Haar) measures. The connection between the representation theory of a locally compact group and that of general Banach algebras proceeds directly from Lebesgue integration with respect to Haar measure on the group.
    • 2012, H. Heyer, Probability Measures on Locally Compact Groups, Springer, page 12:
      A locally compact group is called Lie projective if it is the projective limit of Lie groups with a descending family of compact normal subgroups of satisfying .
    • 2013, Eberhard Kaniuth, Keith F. Taylor, Induced Representations of Locally Compact Groups, Cambridge University Press, page 269:
      Let be a locally compact group and a closed subgroup of , and suppose that and are irreducible representations of and , respectively.

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