Homeomorphic operations

Among the transformations in family G one finds all the symmetry operations, but also all reflections in curved mirrors, nonlinear stretchings, and all continuous distortions of the space. Evidently, all possible homeomorphisms of the 3D space form a group G. Any two such transformations applied consecutively correspond to one such transformation (closure property) the unit element is the... 

By summing the forces at junctions 2 and 3 (the equilibrium positions for Xj and X3) and the torques acting on the eyeball, using Laplace variable analysis about the operating point, the linear homeomorphic model, as shown in Figure 16.4, is derived as... 

Since, for the moment, the separatrix diagram of the critical circle ia supposed to be orientable, the first case (the Mobius strip) is impossible here. The tubular neighbourhood of the surface P. is therefore homeomorphic to a round handle. It is glued to Ca-g precisely in the fashion suggested by the definition of the round-handle -gluing operation (see above). The axes of both feet of the round handle are glued to two smooth circles 71 and 72 drawn on Ba-g by points A and B (Fig. 27) when the point x slides upon S. ... 

---