Topological Spaces

  • John M. LeeEmail author
Part of the Graduate Texts in Mathematics book series (GTM, volume 202)


In this chapter we begin our study in earnest. The first order of business is to build up enough machinery to give a proper definition of manifolds. The chief problem with the provisional definition given in Chapter 1 is that it depends on having an “ambient Euclidean space” in which our n-manifold lives. This introduces a great deal of extraneous structure that is irrelevant to our purposes. Instead, we would like to view a manifold as a mathematical object in its own right, not as a subset of some larger space. The key concept that makes this possible is that of a topological space, which is the main topic of this chapter.


Open Subset Topological Space Limit Point Closed Subset Open Ball 
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Copyright information

© Springer Science and Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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