Definition:Compatible Charts/Smooth
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Definition
Let $M$ be a topological space.
Let $d$ be a natural number.
Let $\struct {U, \phi}$ and $\struct {V, \psi}$ be $d$-dimensional charts of $M$.
$\struct {U, \phi}$ and $\struct {V, \psi}$ are smoothly compatible if and only if their transition mapping:
- $\psi \circ \phi^{-1} : \map \phi {U \cap V} \to \map \psi {U \cap V}$
is of class $C^\infty$.