International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 7, Pages 433-435
doi:10.1155/S016117120100727X
Products of protopological groups
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.
Abstract
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.