Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The Piecewise-Linear Structure of Euclidean Space

John Stallingsa1

a1 Institute for Advanced Study and Princeton University

It is known that, for n ≤3, ‘ought to have’ can truthfully be replaced by ‘has’ (see (4), and (5), Cor. 6·6). In this paper, this conjecture will be proved for n ≥ 5. The only unsolved case then will be in dimension four.

(Received December 19 1961)