Let $M$ be a smooth manifold. Let $H^s(T^2_0M)$ be the Sobolev class of symmetric $0,2$ tensors defined by the class of $0,2$ tensors whose derivatives up to order $s$ exist in the sense of distributions and are square integrable. Since it is a vector space, it can be identified as $\mathbb{R}^n$ for some $n$, equipped with usual topology.
Let $\mathcal{M}^s$ be the subset of $H^s(T^2_0M)$ consisting of Riemannian metrics on $M$. How can I show that it is an open set in $H^s(T^2_0M)$? The usual approach is to construct continuous map whose preimage of some open set in the range of the function is $\mathcal{M}^s$. However, I have no idea how to construct such a map.