Vol. 23, No. 1, 1967

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On uniquely divisible semigroups on the two-cell

John A. Hildebrant

Vol. 23 (1967), No. 1, 91–95

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.

Mathematical Subject Classification
Primary: 22.05
Received: 27 January 1966
Published: 1 October 1967
John A. Hildebrant