  A fibration of ${\mathbb R}^n$ by oriented copies of ${\mathbb R}^p$ is
called skew if no two fibers intersect nor contain parallel directions.
Conditions on $p$ and $n$ for the existence of such a fibration were given by
Ovsienko and Tabachnikov. A classification of smooth fibrations of ${\mathbb
R}^3$ by skew oriented lines was given by Salvai, in analogue with the
classification of oriented great circle fibrations of $S^3$ by Gluck and
Warner. We show that Salvai's classification has a topological variation which
generalizes to characterize all continuous fibrations of ${\mathbb R}^n$ by
skew oriented copies of ${\mathbb R}^p$. We show that the space of fibrations
of ${\mathbb R}^3$ by skew oriented lines deformation retracts to the subspace
of Hopf fibrations, and therefore has the homotopy type of a pair of disjoint
copies of $S^2$. We discuss skew fibrations in the complex and quaternionic
setting and give a necessary condition for the existence of a fibration of
${\mathbb C}^n$ (${\mathbb H}^n$) by skew oriented copies of ${\mathbb C}^p$
(${\mathbb H}^p$).
