Identification Spaces

  • M. A. Armstrong
Part of the Undergraduate Texts in Mathematics book series (UTM)


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.


Topological Space Identification Space Topological Group Orbit Space Identification Topology 
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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • M. A. Armstrong
    • 1
  1. 1.Department of MathematicsUniversity of DurhamDurhamEngland

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