Continuous functions on metric space, M

[roman93]

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!

 

[Stephen Tashi]

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.

 

[micromass]

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.

 

[HallsofIvy]

Since f(p)= p is continuous, one thing that tells you is that M itself is bounded!