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Section Summary
Important ideas that we discussed in this section include the following.
Let \((X,d_X)\) and \((Y, d_Y)\) be metric spaces. A function \(f:X \to Y\) is continuous at \(a \in X\) if, given any \(\epsilon \gt 0\text{,}\) there exists a \(\delta \gt 0\) so that \(d_X(x,a)\lt \delta\) implies \(d_Y(f(x), f(a)) \lt \epsilon\text{.}\)
Let \((X,d_X)\) and \((Y, d_Y)\) be metric spaces. A function \(f:X \to Y\) is continuous if \(f\) is continuous at every point in \(X\text{.}\)
