Square Roots and Continuity in Strictly Linearly Ordered Semigroups on Real Intervals
classification
🧮 math.CA
math.FA
keywords
semigroupreallinearlyorderedsquarestrictlyadditiveadmits
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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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