functional limit

let $\text{[math]}$ and let $\text{[math]}$ be a limit point of $\text{[math]}$ . then we say that
$\text{[math]}$ if for all $\text{[math]}$ there exists some $\text{[math]}$ such that for every $\text{[math]}$ for which $\text{[math]}$ , we have
$\text{[math]}$ we also say $\text{[math]}$ converges to $\text{[math]}$ in such a situation.
[cite:;taken from @analysis_cummings_2019 definition 6.8]