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All the Mathematics You Missed by Lori Pedersen, Thomas A. Garrity

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Chapter 4

Point Set Topology

Basic Object:

Topological spaces

Basic Map:

Continuous functions

Historically, much of point set topology was developed to understand the correct definitions for such notions as continuity and dimension. By now, though, these definitions permeate mathematics, frequently in areas seemingly far removed from the traditional topological space Rn. Unfortunately, it is not at first apparent that these more abstract definitions are at all useful; there needs to be an initial investment in learning the basic terms. In ...

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