Is the disjoint union of an arbitrary number of $n$-manifolds, again a $n$-manifold?
I only found a result that proves this for countably many manifolds.
2026-03-28 09:50:22.1774691422
Disjoint union of manifolds
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That depends upon your definition of manifold, but by the usual definition they are second countable. And that excludes the possibility of being an infinite non-countable union of disjoint manifolds.