smoothly compatible

Definition

Two charts $(U,\varphi)$ and $(V,\psi)$ are said to be smoothly compatible if either $U \cap V = \emptyset$ or transition map $\psi \circ \varphi^{-1}$ is a diffeomorphism.

References

1. J. M. Lee, Introduction to smooth manifolds, Second edition. in Graduate texts in mathematics, no. 218. New York Heidelberg Dordrecht London: Springer, 2013, p. 12.