For each r, the C^r structures on the non-Hausdorff letter Y are in bijection with certain diffeomorphism-group double cosets, yielding uncountably many non-diffeomorphic structures.
Freed and Karen K
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Differentiable structures on a union of two open sets
For each r, the C^r structures on the non-Hausdorff letter Y are in bijection with certain diffeomorphism-group double cosets, yielding uncountably many non-diffeomorphic structures.