What Is Mathematics? : An Elementary Approach to Ideas and Methods by Robbins Herbert & Richard Courant

Author:Robbins, Herbert & Richard Courant [Robbins, Herbert]
Language: eng
Format: mobi
Publisher: Oxford University Press
Published: 1996-05-30T16:00:00+00:00

Fig. 143. Closed surfaces defined by coördination of edges in plane figure.

Fig. 144. Three-dimensional torus defined by boundary identification.

faces of a cube (Fig. 144), we obtain a closed, three-dimensional manifold called the three-dimensional torus. This manifold is topologically equivalent to the space between two concentric torus surfaces, one inside the other, in which corresponding points of the two torus surfaces are identified (Fig. 145). For the latter manifold is obtained from the cube if two pairs of conceptually identified faces are brought together.

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