In this chapter, we extend the notions of neighborhoods, convergent sequences, and continuous functions, which we have studied in the setting of the real line, to more general situations. We are interested especially in the setting of R d , the Euclidean space of dimension d, but it turns out that the means by which we formulate and analyze the notions of continuity and convergence, and related ideas, carry over to much more general settings, with little or no adaptation; as a result, we shall introduce some fairly abstract notions right from the beginning.
KeywordsOpen Subset Topological Space Limit Point Closed Subset Compact Space
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