Remark

If $y \in Y$ is a limit (resp. cluster point) of a mapping $f : X \to Y$ with respect to a filter $\mathfrak{F}$ on $X$, then $y$ is also a limit (resp. cluster point) of every function $g : X \to Y$ which has the same germ as $f$ with respect to $\mathfrak{F}$ (§ 6, no. 9); $y$ is said to be a limit (resp. cluster point) of the germ $\tilde{f}$ of $f$ with respect to $\mathfrak{F}$.