Deane Montgomery quotes

A group which has a simple structure may offer difficult questions when operating as a transformation group. For example, the ways in which a cyclic group of order 2 can operate on a manifold, even on E 3, are far from completely known. (Deane Montgomery)
THEOREM: if G is a locally euclidean, connected, simply connected topological group of dimension n greater than one, then G contains a closed proper subgroup of positive dimension. View quote
Deane Montgomery