The space of all self-homeomorphisms of a two-cell which fix the cell’s boundary is an absolute retract

Mason, W. K.

doi:10.1090/S0002-9947-1971-0286067-9

The space of all self-homeomorphisms of a two-cell which fix the cell’s boundary is an absolute retract
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Trans. Amer. Math. Soc. 161 (1971), 185-205 Request permission

Abstract:

The theorem mentioned in the title is proved. A corollary of the title theorem is: any homeomorphism between two compact subsets of the function space mentioned in the title can be extended to a homeomorphism of the function space onto itself.

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Problems on infinite-dimensional spaces and manifolds