Last edited by Godisgood; Nov 1st 2010 at 06:07 AM.
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Originally Posted by Godisgood Let X_n and y_n be two convergent sequence in the metric space (X,d) with X_n converging to x and y_n converging to y. show that d(x_n, y_n) converges to d(x,y)
Thanks What about
This should get you started. This is half of the inequality.
That is true only if d(*,*) is continous in [x,y]...
Do you know that
There is a well-known theorem for metric spaces:
for any points it is the case that .
Apply that to both terms on the right of