Deane Montgomery

North Carolina · connected1909–1992

American mathematician (1909–1992)

Died in Chapel Hill

mathematician

Quotations with a citation

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.

Recorded without a firm citation

Kept here, labelled, rather than mixed in above.

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.