Note 3 — Chapter I · MANIFOLDS

We need not discuss here the difficult problems that relate to the connectivity of the continua. For instance, a point on a closed line does not divide the line into two parts, and yet the line remains one-dimensional. Problems of this sort pertain to one of the most difficult branches of geometry, namely, Analysis Situs, with which the names of Riemann, Betti and Poincaré are associated.