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Chapter 5: Metric Spaces

The limits we've studied so far have been of sequences and function of real numbers. What about sequences in Rn, or functions of several variables? We could treat all of these situations separately, but if we did, we'd find ourselves proving and reproving the same results over and over. So what we do instead, in this chapter, is to develop an abstarct framework that lets us deal with all of the kinds of limits that we'll use. This is called a metric space. In fact it turns out that this context is general enough to lead us to teh useful example of uniform convergence of sequences of functions, which we'll study more in Chapter 9.

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