Date of Award

1995

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Jimmi Lawson

Abstract

For a topological semigroup S, Lawson constructed a semigroup $\Gamma(S)$ with the property that any local homomorphism defined in a neighborhood of the identity of S to a topological semigroup T extends uniquely to a global homomorphism defined on $\Gamma(S).$ In this work we obtain conditions on S to topologize the semigroup $\Gamma(S)$ via an uniformity such that the extended homomorphism is continuous and such that $\Gamma(S)$ is a topological semigroup. We also investigate a different approach of the problem via the relatively free semigroup RF(U) where U is a suitable neighborhood of the identity of S and show that RF(U) is isomorphic to $\Gamma(S).$.

Pages

41

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