if (x_n) is a sequence that converges uniformly to x and f a continuous fonction
can we say that f(x_n) converges uniformly to f(x)?
thank you
well, this is what I want to show.
(df_n) is the differential operator.
In fact, $\displaystyle f$ is $\displaystyle C^1$ in $\displaystyle R^n$ and $\displaystyle f_n$ is a polynomial function that converges uniformly to $\displaystyle f$. THis is the Weierstrass theorem.
Can I say that $\displaystyle df_n$ converges uniformly to $\displaystyle df$??