Register to reply

Continuous functions on metric space, M

by roman93
Tags: continuous, functions, metric, space
Share this thread:
roman93
#1
Jan30-13, 08:44 AM
P: 14
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!
Phys.Org News Partner Mathematics news on Phys.org
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Stephen Tashi
#2
Jan30-13, 11:33 AM
Sci Advisor
P: 3,296
Quote Quote by roman93 View Post
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
#3
Jan30-13, 11:38 AM
Mentor
micromass's Avatar
P: 18,291
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.

HallsofIvy
#4
Jan31-13, 09:11 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,547
Continuous functions on metric space, M

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


Register to reply

Related Discussions
Help with continuous functions in metric spaces Topology and Analysis 4
Let f be a continuous real function on a metric space X. Let ... Calculus & Beyond Homework 4
Continuous functions on metric spaces with restrictions Calculus & Beyond Homework 6
Construct a continuous function in metric space Calculus & Beyond Homework 4
Continuous functions in metric spaces Differential Geometry 1