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Weak continuity properties of topologized groups

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Abstract

We explore (weak) continuity properties of group operations. For this purpose, the Novak number and developability number are applied. It is shown that if (G, ·, τ) is a regular right (left) semitopological group with dev(G) < Nov(G) such that all left (right) translations are feebly continuous, then (G, ·, τ) is a topological group. This extends several results in literature.

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Authors and Affiliations

  1. School of Computing and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland, 1142, New Zealand

    J. Cao

  2. Institute of Mathematics, Pedagogical University of Slupsk, 76-200, Slupsk, Poland

    R. Drozdowski

  3. Department of Mathematics, Youngstown State University, Youngstwon, Ohio, 44555-0001, USA

    Z. Piotrowski

Authors
  1. J. Cao
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  2. R. Drozdowski
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  3. Z. Piotrowski
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Correspondence to J. Cao.

Additional information

The first author acknowledges the financial support by grant DJ-8899-4120-02 from the Auckland University of Technology, New Zealand. The third author would like to thank for the hospitality of the School of Computing and Mathematical Sciences during his visit to the Auckland University of Technology, New Zealand, in March–April, 2008.

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Cao, J., Drozdowski, R. & Piotrowski, Z. Weak continuity properties of topologized groups. Czech Math J 60, 133–148 (2010). https://doi.org/10.1007/s10587-010-0004-8

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