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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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How many n-dimensional closed submanifolds of $R^n$ have Euler characteristic 1?
It is well-known that the closed $n$-ball has Euler characteristic $1$. Is it true that every closed (i.e., compact), connected $n$-dimensional submanifold (with boundary) of $\mathbb R^n$ having Eule …