  Let $\mathcal{F}$ be any collection of linearly separable sets of a set $P$
of $n$ points either in $\mathbb{R}^2$, or in $\mathbb{R}^3$. We show that for
every natural number $k$ either one can find $k$ pairwise disjoint sets in
$\mathcal{F}$, or there are $O(k)$ points in $P$ that together hit all sets in
$\mathcal{F}$. The proof is based on showing a similar result for families
$\mathcal{F}$ of sets separable by pseudo-discs in $\mathbb{R}^2$. We
complement these statements by showing that analogous result fails to hold for
collections of linearly separable sets in $\mathbb{R}^4$ and higher dimensional
euclidean spaces.

Combinatorics;Computational Geometry;Discrete Mathematics