On the embedding of topological domains into quotient fields

Necessary and sufficient conditions to embed a Hausdorff left Ore domain A in a topological field Q(A) of quotients are given in terms of conditions on an invariant uniformity topologizing the multiplicative semigroup A* of A. The categorical aspects of such an embedding are discussed, and a new proof of S. Warner's theorem on the embedding of a left Ore domain as an open subring of a topological field of quotients is given.This work comprises part of the author's doctoral dissertation submitted to SUNY at Buffalo. The author wishes to thank Professor Dov Tamari for suggesting this problem.