  For a set $L$ of positive integers, a set system $\mathcal{F} \subseteq
2^{[n]}$ is said to be $L$-close Sperner, if for any pair $F,G$ of distinct
sets in $\mathcal{F}$ the skew distance $sd(F,G)=\min\{|F\setminus
G|,|G\setminus F|\}$ belongs to $L$. We reprove an extremal result of Boros,
Gurvich, and Milani\v c on the maximum size of $L$-close Sperner set systems
for $L=\{1\}$ and generalize to $|L|=1$ and obtain slightly weaker bounds for
arbitrary $L$. We also consider the problem when $L$ might include 0 and
reprove a theorem of Frankl, F\"uredi, and Pach on the size of largest set
systems with all skew distances belonging to $L=\{0,1\}$.
