# Continuous functions on metric space, M

by roman93
Tags: continuous, functions, metric, space
 P: 15 If every continuous function on M is bounded, what does this mean? I am not sure what this function actually is... is it a mapping from M -> M or some other mapping? Is the image of the function in M? Any help would be greatly appreciated!
P: 2,892
 Quote by roman93 is it a mapping from M -> M or some other mapping?
I suggest that you explain where you saw this statement and quote it exactly.
 PF Patron Sci Advisor Thanks Emeritus P: 15,673 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.
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