Let $X$ be a compact space and $(A_n)$ a sequence of closed sets in $X$. Let $H-\lim_nA_n=A$ (the Hausdorff limit of $(A_n)$). Does $H-\lim_n(X\setminus A_n)$ exists? If yes, how is it related to $X\setminus A$? Here $X\setminus S$ is the complement of a set $S$ in $X$ with respect to $X$.

Ivo Lah is a slovenian mathematican mostly known for introducing Lah numbers $$ L(n,k) = \left\lfloor n \atop k \right\rfloor := \binom{n-1}{k-1}\frac{n!}{k!}. $$ His original paper on this subject has the reference Lah, Ivo (1954). "A new kind of numbers and its application in the actuarial mat...