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Continuous functions on metric space, M 
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#1
Jan3013, 08:44 AM

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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! 


#2
Jan3013, 11:33 AM

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#3
Jan3013, 11:38 AM

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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. 


#4
Jan3113, 09:11 AM

Math
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Continuous functions on metric space, M
Since f(p)= p is continuous, one thing that tells you is that M itself is bounded!



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