# continuous function betweem two metric spaces

• November 18th 2010, 02:53 AM
1234567
continuous function betweem two metric spaces

Attachment 19755

Thanks
• November 18th 2010, 04:02 AM
FernandoRevilla
Hint:

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

Regards.

Fernando Revilla
• November 18th 2010, 10:26 AM
Jose27
Quote:

Originally Posted by 1234567
Personally while the other two responses are correct I think it's easier to notice that if $\|f-g\|_{\infty}<\frac{\varepsilon}{4}$ then $\displaystyle \left|f(1)-g(1)+(f(0)-g(0))-(2f(\frac{1}{2})-g(\frac{1}{2}))\right|\leqslant |f(1)-g(1)|+|f(0)-g(0)|+2|f(\frac{1}{2})-g(\frac{1}{2})|\leqslant 4\|f-g\|_{\infty}<\varepsilon$.