Category:Compatible Atlases
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This category contains results about Compatible Atlases.
Definitions specific to this category can be found in Definitions/Compatible Atlases.
Let $M$ be a topological space.
Let $\mathscr F, \mathscr G$ be $d$-dimensional atlases of class $C^k$ on $M$.
Definition 1
$\mathscr F, \mathscr G$ are $C^k$-compatible if and only if their union $\mathscr F \cup \mathscr G$ is an atlas of class $C^k$.
Definition 2
$\mathscr F$ and $\mathscr G$ are $C^k$-compatible if and only if every pair of charts $\struct {U, \phi} \in \mathscr F$ and $\struct {V, \psi} \in \mathscr G$ are $C^k$-compatible.
Pages in category "Compatible Atlases"
The following 2 pages are in this category, out of 2 total.