A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may change in different coordinates. This even occurs in Euclidean space R^3, where any rotation of the usual x, y, and z axes gives another set of coordinates. For example, on the sphere, person A at the equator can use the usual directions of north, south, east, and west, but person B at the north pole must use something else. However, both A and B can describe the region in between them in their coordinate charts. A transition function would then describe how to go from the coordinate chart for A to the coordinate chart for B.

bundle | Čech cohomology | coordinate chart | manifold | tangent bundle | trivialization | vector bundle