I have some problems to apply normal convergence of series of functions in any vector space. In fact $(f_{n})$ is a sequence of differentiable functions defined from a topological space $X$ to a normed vector space $Y$, that is normally convergent, I want to ask if the sequence of derivatives $(f_{n}')$ converges normally as well?
Normal convergence
1
$\begingroup$
functional-analysis
convergence
derivatives