First, I know (or I think I know...) the definition of fiber bundle, be it in the smooth or topological category. Here is my situation, which is kind of between the two: I have a smooth manifold $E$, a topological manifold $X$, a continuous surjective map $p : E \rightarrow B$ such that in local charts, $p$ is a linear projection.
If both $E$ and $B$ were topological manifolds, that would be equivalent to saying that $p$ is a fibre bundle in the topological category. If both $E$ and $B$ where both smooth, $p$ would be a fibre bundle in the smooth category.
Is there a standard terminology for my "half-way through" case ? (I emphasize that my property is stronger than being a (topological) fibre bundle).