Let X,Y be metric spaces with metrics d1,d2 respectively.

let f:X-->Y be a function with the property that for all pair of points x1,x2 of X, d2(f(x1),f(x2))=d1(x1,x2).

Show that f is an imbedding..

thnak you in advance

Printable View

- Nov 16th 2009, 03:21 AMmath.djIsometric imbedding
Let X,Y be metric spaces with metrics d1,d2 respectively.

let f:X-->Y be a function with the property that for all pair of points x1,x2 of X, d2(f(x1),f(x2))=d1(x1,x2).

Show that f is an imbedding..

thnak you in advance - Nov 16th 2009, 04:00 AMSampras
- Nov 16th 2009, 04:09 AMmath.dj
thank you for ur response..but we have not yet come across this definition of embedding..

- Nov 18th 2009, 02:18 AMmath.dj
i need a little help..i have shown that f is injective and continuous.now i need to show that g:X-->f(x) is a homeomorphism..how do i show g and g^-1(that is g inverse) are continuous..