Products of protopological groups
Montgomery and Zippin saied that a group is approximated by Lie groups if every neighborhood of the identity contains an invariant subgroup such that 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.