While reading the second edition of Munkres' Topology, I came across this (page 129):
Theorem 21.1 Let $f: X \rightarrow Y$; let $X$ and $Y$ be metrizable with metrics $d_X$ and $d_Y$, respectively. Then continuity of $f$ is equivalent to the requirement that given $x \in X$ and given $\epsilon > 0$, there exists $\delta > 0$ such that $d_X(x,y) \implies d_Y(f(x), f(y)) < \epsilon$.
Shouldn't the last part be $d_X(x,y) < \delta \implies d_Y(f(x), f(y)) < \epsilon$ ? I've looked at the errata here but didn't find mention of this. am i missing something? Thanks for any help/clarification. :)