Geodesic
Local Contractibility of the Homeomorphism Group of~$\mathbb R^n$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 201-215

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The goal of this paper is to give a modified exposition of the main part of the proof of the local contractibility theorem. The derivation of general theorems from the special case of Euclidean space remains intact. The exposition is rather detailed and is aimed, in particular, at correcting an inaccuracy in the original proof. 
@article{TM_2008_263_a13,
     author = {A. V. Chernavskii},
     title = {Local {Contractibility} of the {Homeomorphism} {Group} of~$\mathbb R^n$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {201--215},
     publisher = {mathdoc},
     volume = {263},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_263_a13/}
}
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A. V. Chernavskii. Local Contractibility of the Homeomorphism Group of~$\mathbb R^n$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 201-215. http://geodesic.mathdoc.fr/item/TM_2008_263_a13/