Let $X$ be a compact surface of genus $g \geq 1$. Then it is a well known fact that the space of embeddings into $\mathbb{R}^{\infty}$ is contractible. The proof uses Whitney's embedding theorem. Moreover, this space a CW-complex by simplicial approximation on embedding spaces $X \rightarrow \mathbb{R}^n$.

Is there an article or text book that I may refer to. All papers I read just mention it without proof.