  We introduce a geometric generalization of Hall's marriage theorem. For any
family $F = \{X_1, \dots, X_m\}$ of finite sets in $\mathbb{R}^d$, we give
conditions under which it is possible to choose a point $x_i\in X_i$ for every
$1\leq i \leq m$ in such a way that the points $\{x_1,...,x_m\}\subset
\mathbb{R}^d$ are in general position. We give two proofs, one elementary proof
requiring slightly stronger conditions, and one proof using topological
techniques in the spirit of Aharoni and Haxell's celebrated generalization of
Hall's theorem.
