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Square roots and continuity in strictly linearly ordered semigroups on real intervals

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Abstract

In this article we show that the semigroup operation of a strictly linearly ordered semigroup on a real interval is automatically continuous if each element of the semigroup admits a square root. Hence, by a result of Aczél, such a semigroup is isomorphic to an additive subsemigroup of the real numbers.

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Authors and Affiliations

  1. Institute of Applied Analysis, Ulm University, 89069,  Ulm, Germany

    Jochen Glück

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  1. Jochen Glück
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Correspondence to Jochen Glück.

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Communicated by Jimmie D. Lawson.

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Glück, J. Square roots and continuity in strictly linearly ordered semigroups on real intervals. Semigroup Forum 89, 491–500 (2014). https://doi.org/10.1007/s00233-014-9589-9

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  • DOI: https://doi.org/10.1007/s00233-014-9589-9

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