Suppose we have a manifold $M$ and an atlas consisting of two charts $U_1 , U_2$ which are disjoint. Does this cause a problem or is our life easier? I would guess that smoothness follows vacuously but I want to make sure.
2026-04-13 18:00:57.1776103257
If the charts comprising an atlas are disjoint, is the smoothness of transition functions trivial?
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