Let be an open subset of and a -dimensional slice of is an subset of the form
(i.e. the last variables are constant).
Note: It doesn’t necessarily have to be the last coordinates, just some subset of them.
Let be a manifold with a chart on . A subset is called a -slice of if is a -slice. If is a subset such that every point of is contained in the domain of a chart for such that is a single -slice in , then any such chart is called a slice chart for in the coordinates are called slice coordinates.