  In the paper we introduce the notions of a singular fibration and a singular
Seifert fibration. These notions are natural generalizations of the notion of a
locally trivial fibration to the category of stratified pseudomanifolds. For
singular foliations defined by such fibrations we prove a de Rham type theorem
for the basic intersection cohomology introduced the authors in a recent paper.
One of important examples of such a structure is the natural projection onto
the leaf space for the singular Riemannian foliation defined by an action of a
compact Lie group on a compact smooth manifold.
