|Jan30-13, 08:44 AM||#1|
Continuous functions on metric space, M
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!
|Jan30-13, 11:33 AM||#2|
|Jan30-13, 11:38 AM||#3|
A map [itex]f:X\rightarrow M[/itex] 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 [itex]x\in X[/itex] and an [itex]\varepsilon>0[/itex] such that [itex]f(X)\subseteq B(f(x),\varepsilon)[/itex].
This is what I would call bounded. But you will need to specify the context.
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