Square Roots and Continuity in Strictly Linearly Ordered Semigroups on Real Intervals
arXiv:1402.7297 · doi:10.1007/s00233-014-9589-9
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.