Uniformly R-factorizable groups
by
Gerald Itzkowitz
Queens College/C.U.N.Y.,USA
Coauthors: V.V. Tkachuk (Queens College,USA and Universidad Autonoma Metropolitana, Mexico)

A topological group G is left uniformly -factorizable if for every left uniformly continuous real valued function defined on G there is a continuous homomorphism h:G M, where M is a second countable group such that f = g h for some left uniformly continuous function g:M . A characterization is given of such groups. We prove that a group G is left uniformly -factorizable iff it is _0-bounded. This should be contrasted with the case of -factorizable groups studied by M.G. Tkachenko. Tkachenko showed that -factorizable groups are _0-bounded, but the converse is false. Tkachenko's work thus shows that -factorizable groups are left uniformly -factorizable. Another corollary of our work is that left and right uniformly -factorizable are equivalent so this property can be called simply `uniformly

Date received: June 2, 2002