On uniquely divisible semigroups on the two-cell
John A. Hildebrant · Pacific Journal of Mathematics · 1967
A topological semigroup S is a Hausdorff space together with a continuous associative multiplication on S. A semigroup S is said to be uniquely divisible if each element of S has unique roots of each positive integral order in S. The present paper concerns uniquely divisible semigroups on the two-cell.The main result of this paper is a statement of equivalent conditions for a commutative uniquely divisible semigroup on the two-cell to be the continuous homomorphic image of the cartesian product of two threads.This result is applied to determine the structure of commutative uniquely divisible semigroups on the two-cell whose idempotent set consists of a zero and an identity.