Geodesic
On the $l_2$-stability of the spaces of homeomorphisms of metric spaces
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1982), pp. 37-40

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The space $H(M)$ of homeomorphisms of a metric space $M$ is homeomorphic to the product $H(M)\times l_2$ if there exists an embedding $\varphi\colon K\times[0,1]\to M$ of the product of a metrizable compact space $K$ and the segment $[0,1]$ into the space $M$ such that $\operatorname{Int}\varphi(K\times[0,1])\ne\varnothing$. 
@article{VMUMM_1982_1_a10,
     author = {V. N. Basmanov},
     title = {On the $l_2$-stability of the spaces of homeomorphisms of metric spaces},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {37--40},
     publisher = {mathdoc},
     number = {1},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_1_a10/}
}
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V. N. Basmanov. On the $l_2$-stability of the spaces of homeomorphisms of metric spaces. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1982), pp. 37-40. http://geodesic.mathdoc.fr/item/VMUMM_1982_1_a10/