2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146659In 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.22 pagesDifferential GeometryAlgebraic Topology14F40; 5312text