A continuous choice of the sense of handedness in a space. A line may be assigned one of two directions. A simple, closed plane curve may be positively oriented or assigned an outward-pointing normal. Left- and right-handed systems are two different orientations of 3-dimensional space. Two bases of ℝⁿ give the same orientation if the change of basis matrix has positive determinant. Some spaces, such as the Möbius band and Klein bottle, are non-orientable and so have no orientation. See also Stokes’ Theorem.