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.



Reference question: space of embeddings
See page 86 of:


Peter W. Michor: Gauge theory for fiber bundles. Monographs and Textbooks in Physical Sciences, Lecture Notes 19, Bibliopolis, Napoli, (1991), 107 pp. MR 94a:53056. Zbl 953.53001 
[(pdf)](http://www.mat.univie.ac.at/~michor/gaubook.pdf) 


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)](http://www.mat.univie.ac.at/~michor/apbookh-ams.pdf).


