# It is not clear to me if the disjoint union of a $d_{1}$-manifold and a $d_{2}$-manifold is still a manifold? [duplicate]

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?

## marked as duplicate by Santana Afton, Yanior Weg, Maximilian Janisch, Don Thousand, ShaileshOct 5 at 2:48

This is true if and only if $$d_1=d_2$$. The definition of a manifold mentions only one dimension, which must be consistent across all charts.