THEOREM: if G is a locally euclidean, connected, simply connected topo…

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.

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“THEOREM: if G is a locally euclidean, connected, simply conn…” Deane Montgomery. Carolina Quotes, record CQ-245459F713. https://carolinaquotes.com/quote/245459f713

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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.

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