TOWARDS A NEW CONSTRUCTION OF FREE TOPOLOGICAL GROUPS

Abstract

It is shown that the free topological group over a completely regular space (in its right uniformity) can be obtained as a uniform quotient of a free semi-uniform monoid, i.e., a monoid with respect to the semi-uniform product in the sense of Isbell. A complete description of the algebraic and topological structure of these monoids is given and the problem is posed of how to describe the uniformity of free semi-uniform monoids explicitly.