Many interesting spaces can be constructed as follows. Begin with a fairly simple topological space X and produce a new space by identifying some of the points of X. We have already made use of this process: in Chapter 1 we had occasion to construct various surfaces and we showed how to obtain the Möbius strip, the torus, and the Klein bottle by making appropriate identifications of the edges of a rectangle. We propose to examine the construction of the Möbius strip in more detail and explain how to use the topology of the rectangle in order to make the Möbius strip into a topological space. The Möbius strip, when defined in this way, will be an example of an identification space.
KeywordsTopological Space Identification Space Topological Group Orbit Space Identification Topology
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