Montgomery and Zippin saied that a group is approximated by Lie
groups if every neighborhood of the identity contains an
invariant subgroup H such that G/H is topologically
isomorphic to a Lie group. Bagley, Wu, and Yang gave a similar
definition, which they called a pro-Lie group. Covington extended
this concept to a protopological group. Covington showed that
protopological groups possess many of the characteristics of
topological groups. In particular, Covington showed that in a
special case, the product of protopological groups is a
protopological group. In this note, we give a
characterization theorem for protopological groups and use it to
generalize her result about products to the category of all
protopological groups.