One-dimensional foliations on topological manifolds

Let $X$ be an $(n+1)$-dimensional manifold, $\mathrm{\Delta }$ be a one-dimensional foliation on $X$, and $p:X\to X\mathrm{/}\mathrm{\Delta }$ be a quotient map. We will say that a leaf $\omega$ of $\mathrm{\Delta }$ is special whenever the space of leaves $X / \Delta$isnotHausdorffat$\omega$. We present necessary and sufficient conditions for the map $p:X\to X\mathrm{/}\mathrm{\Delta }$ to be a locally trivial fibration under assumptions that all leaves of $\mathrm{\Delta }$ are non-compact and the family of all special leaves of $\mathrm{\Delta }$ is locally finite.