Square Roots and Continuity in Strictly Linearly Ordered Semigroups on Real Intervals
Classical Analysis and ODEs
2014-05-07 v1 Functional Analysis
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.
Cite
@article{arxiv.1402.7297,
title = {Square Roots and Continuity in Strictly Linearly Ordered Semigroups on Real Intervals},
author = {Jochen Glück},
journal= {arXiv preprint arXiv:1402.7297},
year = {2014}
}