We comment van Douwen's problems on the Bohr topology of the abelian groups raised in his paper (The maximal totally bounded group topology on G and the biggest minimal G-space for Abelian groups G) as well as the steps in the solution of some of them. New solutions to two of the resolved problems are also given.
Mathematics Subject Classification. 05D10 20K45 (22A05 54H11).
Keywords. Bohr topology, homeomorphism, dimension, Ramsey theorem,
partition theorem.
Comments. This article is in final form.