Let $M$ and $N$ be smooth, i.e. $C^infty$, manifolds. Suppose that $M$ is compact. Then for every $k geq 0$ it is well known that $$C^k(M,N)$$ admits the structure of a smooth Banach manifold. I am interested in the continuous case, i.e. $k = 0$. I think that then one can drop the regularity of $M$ and $N$ and still get a Banach manifold $$C(M,N)$$ as one constructs the charts via an exponential map. My question: Is $C(M,N)$ a Banach manifold also in the case where $M$ and $N$ are merely topological manifolds, i.e. $C^0$ manifolds? I mean if $M$ and $N$ admit a $C^1$ structure or equivalently a $C^infty$ structure, then the statement is obvious, but this is not always the case.