  The topological Tverberg theorem states that given any continuous map
$f\colon\Delta^{(d+1)(r-1)}\to\mathbb{R}^d$, there are pairwise disjoint faces
$\sigma_1,\ldots,\sigma_r$ of $\Delta^{(d+1)(r-1)}$ such that
$f(\sigma_1)\cap\cdots\cap f(\sigma_r)\ne\emptyset$ whenever $r$ is a prime
power. We generalize this theorem to a continuous map from a certain CW complex
into a Euclidean space.
