Abstract
A new proof is given of the unpublished results of Morlet on the relation between the homeomorphism group and the diffeomorphism group of a smooth manifold. In particular, the result ${\operatorname {Diff}}({D^n},\partial ) \simeq {\Omega ^{n + 1}}({\text {Top}_n}/{O_n})$ is obtained. The main technique is fibrewise smoothing.
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