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 $\Gamma(S).$.
Recommended Citation
Gonzalez, Genaro Segundo, "Locally Generated Semigroups." (1995). LSU Historical Dissertations and Theses. 6066.
https://repository.lsu.edu/gradschool_disstheses/6066
Pages
41
DOI
10.31390/gradschool_disstheses.6066