  We show that a suitable ring with a ``nice'' topology, in which convergent
limits of units are units, is an \aleph_0-exchange ring. We generalize the
argument to show that a semi-regular ring, R, with a ``nice'' topology, is a
full exchange ring. Putting these results in the language of modules, we show
that a cohopfian module with finite exchange has countable exchange. Also, all
modules with Dedekind-finite, semi-regular endomorphism rings are full exchange
modules.
