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Homotopy theory, homological algebra, algebraic treatments of manifolds.

66 votes
8 answers
10k views

What are the open subsets of $\mathbb{R}^n$ that are diffeomorphic to $\mathbb{R}^n$

I would like to know if there is a known necessary and sufficient property on an open subset of $\mathbb{R}^n$ to be diffeomorphic to $\mathbb{R}^n$ : For example : Are all open star-shaped subsets o …