Summary

Section Summary

Important ideas that we discussed in this section include the following.

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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 $ϵ > 0,$ there exists a $δ > 0$ so that $d_{X} (x, a) < δ$ implies $d_{Y} (f (x), f (a)) < ϵ .$
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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 $X .$