# Reference question: space of embeddings

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.

It is for $\ell^2$ there also with a universal Ehresmann connection. The proof adapts to $\mathbb R^{(\infty)}$ as used in section 47 of (here).