1. ## Simply Convergence

let $(f _n)_n \subset C^1((0,1), \Re)$ be a convergent sequence $f (0,1) \rightarrow \Re$
assume that $(f _n)_n \subset C^1 ((0,1), \Re)$ converges simply to $g=1$.
Do we have $f \in C^1\left((0,1), \Re \right)$ ?

2. ## Re: Simply Convergence

Could you clarify in which sense the sequence (f_n) converge to f?

3. ## Re: Simply Convergence

Originally Posted by raheem
let $(f _n)_n \subset C^1((0,1), \Re)$ be a convergent sequence $f (0,1) \rightarrow \Re$
What does this last part mean? How is f connected with $\displaystyle f_n$?

assume that $(f _n)_n \subset C^1 ((0,1), \Re)$ converges simply to $g=1$.
Do we have $f \in C^1\left((0,1), \Re \right)$ ?