(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to show that a distance preserving map is 1:1 and onto. The 1:1 part was easy, but I'm stuck on proving it's onto...

2. Relevant equations

X is compact

T(X)[itex]\subseteq[/itex]X

THere's a hint saying to consider a point y in X\T(X) and consider the minimum distance

between y and x[itex]\in[/itex] T(X) (the infinum of d(x,y) for all x[itex]\in[/itex] T(X) where d is an undefined metric, and call it deltA)

Then it says to consider the sequence

y_{n}=T^{n}(y)

3. The attempt at a solution

Because X is compact, and y_{n}is a subset of X, it must be bounded (I think?) and have a convergent subsequence, and inf(d(T^n(y),T^n(x))=delta for all n (and x_n=T^n(x) will also have a convergent subsequence). Show that the limits of y_n and x_n provide a contradiction?

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# Homework Help: Show that a distance preserving map T:X->X is onto

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