Metrizable topologies and admissible algebras

TL;DR

This paper establishes a precise criterion for embedding metrizable groups into semigroup compactifications via uniformly continuous functions, extending previous theorems and employing advanced techniques.

Contribution

It introduces a necessary and sufficient condition for such embeddings, generalizing earlier results and enhancing understanding of metrizable group compactifications.

Findings

Provides a complete characterization of embeddability conditions.

Generalizes previous theorems by Ben Yaacov, Berenstein, and Ferri.

Employs novel techniques to connect group topology with algebraic structures.

Abstract

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).