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Identification Spaces

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

Abstract

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.

Keywords

Topological Space Identification Space Topological Group Orbit Space Identification Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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