# Continuous functions on metric space, M

by roman93
Tags: continuous, functions, metric, space
 Mentor P: 18,291 A map $f:X\rightarrow M$ where X is a set and M is a metric space, is called bounded if the image f(X) is bounded. This means that there is an $x\in X$ and an $\varepsilon>0$ such that $f(X)\subseteq B(f(x),\varepsilon)$. This is what I would call bounded. But you will need to specify the context.