THE MAXIMAL TOTALLY BOUNDED GROUP TOPOLOGY ON G AND THE BIGGEST MINIMAL G-SPACE, FOR ABELIAN GROUPS-G

For an Abelian (abstract) group G let bG denote the Bohr-compactification of G and let G* denote G as topological subgroup of bG, or, equivalently, let G* be G with its maximal totally bounded group topology. Our main result says that G* has "many" discrete C-embedded subspaces which are C*-embedded in bG. A consequence is that no sequence in G* convergences to a point of bG. As an application we get information about BG, the unique (up to isomorphism) biggest G-space, for (abstract) Abelian G. We show that π(BG) > |G| and |BG| = exp2|G|. For countable Abelian G this tells us BG is not the absolute of ω2. © 1990.