International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 7, Pages 433-435

Products of protopological groups

Julie C. Jones

Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504, LA, USA

Received 30 March 2001

Copyright © 2001 Julie C. Jones. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.