If $M$ and $N$ are manifolds and $M$ is compact, it is straightforward to show that the space $C^0(M,N)$ of continuous maps from $M$ to $N$ is locally path-connected when equipped with the compact-open topology. (Presumably the conclusion holds more generally.)
However, I'd like to be able to point to a reference. Are there any accessible references on the topology of mapping spaces that describe properties like this (or offer something stronger, like a proof that $C^0(M,N)$ is a Banach manifold)?