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The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.

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The closure of the set of injective continuous functions

Kuratowski proved in Sur les théorèmes du „plongement" dans la théorie de la dimension. Fundamenta Mathematicae 28.1 (1937): 336-342 that the set of embeddings of an at most $n$-dimensional separable …
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