Metrizable topologies and admissible algebras

We provide a necessary and sufficient condition for the embeddability of a metrizable group into semigroup compactifications associated to uniformly continuous functions. Our result employs a technique used by I. Ben Yaacov, A. Berenstein and S. Ferri, and generalizes a theorem by them. This paper is part of the author’s Ph.D. dissertation written under the supervision of Stefano Ferri and Jorge Galindo at Universidad de los Andes (Bogot'a-Colombia).