While it is clear that a disjoint union of two $d$-manifolds is a $d$-manifold, it is not clear to me if the disjoint union of a $d_1$-manifold and a $d_2$-manifold is still a manifold and if yes under some conditions then what is its dimension?
Most definitions of manifolds exclude the disjoint union of manifolds of different dimension from being a manifold.
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2 years ago