 Hitting set

A set $H$ is a hitting set for a set family $\mathcal{F}$ if $H\cap A\ne \varnothing$ for every $A\in \mathcal{F}$. Every set is a hitting set for an empty set family; none is a hitting set for a family containing the empty set. Bounded hitting sets permit finite certificates for some infinite set families, as in the bounded-size transversal kernel.