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AUTOMATIC CONTINUITY OF ABSTRACT HOMOMORPHISMS BETWEEN LOCALLY COMPACT AND POLISH GROUPS

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Abstract

We prove results about automatic continuity and openness of abstract surjective group homomorphisms \( K\overset{\varphi }{\to }G, \) where G and K belong to a certain class К of topological groups, and where the kernel of φ satisies a certain topological countability condition. Our results apply in particular to the case where G is a semisimple Lie group or a semisimple compact group, and where К is either the class of all locally compact groups or the class of all Polish groups.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Münster, Einsteinstraβe, 62 48149, Münster, Germany

    O. BRAUN & L. KRAMER

  2. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraβe 7, 64289, Darmstadt, Germany

    KARL H. HOFMANN

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  1. O. BRAUN
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  2. KARL H. HOFMANN
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  3. L. KRAMER
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Correspondence to L. KRAMER.

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L. Kramer Partially supported by SFB 878.

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BRAUN, O., HOFMANN, K.H. & KRAMER, L. AUTOMATIC CONTINUITY OF ABSTRACT HOMOMORPHISMS BETWEEN LOCALLY COMPACT AND POLISH GROUPS. Transformation Groups 25, 1–32 (2020). https://doi.org/10.1007/s00031-019-09537-4

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