Free constructions for topological semigroups
by
J.D. Lawson
Louisiana State University

A topological semigroup S with identity e is said to be freely locally generated if for every continuous local homomorphism defined on a neighborhood N of e into a topological semigroup T, there exists a unique continuous homomorphism h:S to T that agrees with the local homomorphism on some neighborhood of e. It is a standard fact that a connected, locally connected topological group is freely locally generated if and only if it is its own universal cover. But in general the theories of free local generation and of universal covering diverge for topological semigroups. In this talk we give some results and open problems concerning the problem of constructing a freely locally generated semigroup for a given topological semigroup or local semigroup.

Date received: February 11, 2004