Free Topological Groups

Abstract

0. Introduction. In [3; 6; 11] the basic questions of the existence and of the uniqueness of free topological and free topological abelian groups are discussed. Below we present a different approach to these questions and then indicate the consequences of this approach. Whereas M arkov [1 ] resorts to norms and multinorms, Graev [3 ] to metrics and Kakutani [6] to topological products of large families of groups, we use very special groups of homomorphisms. Inasmuch as our construction may be viewed as a topological product, retopologized, our ideas are most closely related to those of Kakutani.