Abstract
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.
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© 2011 Springer Science and Business Media, LLC
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Lee, J.M. (2011). Topological Spaces. In: Introduction to Topological Manifolds. Graduate Texts in Mathematics, vol 202. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7940-7_2
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DOI: https://doi.org/10.1007/978-1-4419-7940-7_2
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