One-dimensional foliations on topological manifolds

Let X be an (n+1)-dimensional manifold, Δ be a one-dimensional foliation on X, and p : X ! X/Δ be a quotient map. We will say that a leaf ! of Δ is special whenever the space of leaves X/Δ is not Hausdorff at !. We present necessary and sufficient conditions for the map p : X ! X/Δ to be a locally trivial fibration under assumptions that all leaves of Δ are non-compact and the family of all special leaves of Δ is locally finite.