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Variations with Möbius-band, compact 2- and 3-spaces. (English) Zbl 1274.51004

Summary: The Möbius band, as a one-sided surface with its circle boundary, is a nice attractive phenomenon, which calls our attention to topology as a modern branch of mathematics. Thus the projective plane, Klein bottle, cylinder, torus, their generalizations in dimensions 2 and 3, lead us to the concept of spaceforms, or compact manifolds. These may model our real world with different metrics, e.g. Euclidean, spherical and Bolyai-Lobachevsky or hyperbolic metrics. Moreover, other possibilities also occur, indicated in this lecture.

MSC:

51B10 Möbius geometries
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