Hi can some please help me with the following problem:

Attachment 19755

Thanks

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- Nov 18th 2010, 02:53 AM1234567continuous function betweem two metric spaces
Hi can some please help me with the following problem:

Attachment 19755

Thanks - Nov 18th 2010, 04:02 AMFernandoRevilla
:__Hint__

Prove: $\displaystyle (f_n)\rightarrow f \Rightarrow (\Delta f_n)\rightarrow \Delta f$.

Regards.

Fernando Revilla - Nov 18th 2010, 10:26 AMJose27
- Nov 18th 2010, 02:00 PMDrexel28
Personally while the other two responses are correct I think it's easier to notice that if $\displaystyle \|f-g\|_{\infty}<\frac{\varepsilon}{4}$ then $\displaystyle \displaystyle \left|f(1)-g(1)+(f(0)-g(0))-(2f(\frac{1}{2})-g(\frac{1}{2}))\right|\leqslant |f(1)-g(1)|+|f(0)-g(0)|+2|f(\frac{1}{2})-g(\frac{1}{2})|\leqslant 4\|f-g\|_{\infty}<\varepsilon$.

- Nov 19th 2010, 12:33 PM1234567
Yes the method that Drexel28 is far the easy way to show this, thanks ;)