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arXiv · 1402.7297

Square Roots and Continuity in Strictly Linearly Ordered Semigroups on Real Intervals

Jochen Glück
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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 Acz\'el, such a semigroup is isomorphic to an additive subsemigroup of the real numbers.

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Jochen Glück. 2014-02-27. Square Roots and Continuity in Strictly Linearly Ordered Semigroups on Real Intervals. https://doi.org/10.1007/s00233-014-9589-9

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