Isometric

Show that C[0,1] and C[a,b] are isometric.
Solution:
A mapping T of X into X' is said to be isometric if for all x, y in X
d'(Tx,Ty)=d(x,y)
C is continous [0,1] and [a,b] closed interval..
The distance on Function space C[a,b] is d(x,y)=max|x(t)-y(t)|

I couldnt procced from here....i need some help....

thanks

Quote:

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Originally Posted by kinkong

Show that C[0,1] and C[a,b] are isometric.
Solution:
A mapping T of X into X' is said to be isometric if for all x, y in X
d'(Tx,Ty)=d(x,y)
C is continous [0,1] and [a,b] closed interval..
The distance on Function space C[a,b] is d(x,y)=max|x(t)-y(t)|

I couldnt procced from here....i need some help....

thanks

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What if you did a mapping that bijectively took in an increasing way, call this , and you considered defined by ?

Thank u very much...
But how can we prove that the map is bijective...i mean how can we see that it is one-to-one and onto...

Quote:

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Originally Posted by kinkong

Thank u very much...
But how can we prove that the map is bijective...i mean how can we see that it is one-to-one and onto...

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Have you tried to prove it?

yes i thought about it..but i couldnt find a way...please can u help me...