In Allen Hatchers short exposition of the Madsen-Weiss Theorem he defines the topology on the space $\mathcal{C}^n$ of smooth oriented properly embedded $d$-dimensional submanifolds of $\mathbb{R}^n$ on page 6 with the help of the

"standard $C^\infty$ topology on the space of d-dimensional smooth compact submanifolds of B that are properly embedded (meaning that the intersection of the submanifold with $\partial B$ is the boundary of the submanifold, and this is a transverse intersection)",

where $B$ is a closed ball centered in the origin.

I am searching for a reference or an explicit definition of the "standard topology" Hatcher is referring to.