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Any Semitopological Group that is Homeomorphic to a Product of Čech-Complete Spaces is a Topological Group

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Abstract

A semitopological group (topological group) is a group endowed with a topology for which multiplication is separately continuous (multiplication is jointly continuous and inversion is continuous). In this paper we answer (Arhangel’skii et al., Math Maced 8:1–19, 2010, Problem 10.4), by showing that if (G, ·, τ) is a semitopological group and (G, τ) is homeomorphic to a product of Čech-complete spaces, then (G, ·, τ) is a topological group.

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Authors and Affiliations

  1. Department of Mathematics, The University of Auckland, Private Bag, 92019, Auckland, New Zealand

    Warren B. Moors

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  1. Warren B. Moors
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Correspondence to Warren B. Moors.

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In celebration of Petar S. Kenderov’s 70th Birthday.

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Moors, W.B. Any Semitopological Group that is Homeomorphic to a Product of Čech-Complete Spaces is a Topological Group. Set-Valued Var. Anal 21, 627–633 (2013). https://doi.org/10.1007/s11228-013-0252-5

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  • DOI: https://doi.org/10.1007/s11228-013-0252-5

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