Solution
= Solution
<Continuity> at $x$ means that for every $\varepsilon>0$ there is $\delta>0$ such that $d_X(x,y)<\delta$ implies $d_Y(f(x),f(y))<\varepsilon$ for every $y\in X$. Equivalently, the <inverse element>[inverse] image of each neighborhood of $f(x)$ is a neighborhood of $x$.