condition may be equivalently expressed by where is the projection onto the first coordinates. The chart is then obviously unique. In view of the above property, the fibered coordinates of a fiber chart are usually denoted by where the coordinates of the corresponding chart on are then denoted, with the obvious convention, by where Conversely, if a surjection admits a fibered atlas, then is a fibered manifold. Local trivialization and fiber bundles Let be a fibered manifold and any manifold. Then an open covering of together with maps called trivialization maps, such that is a local trivialization with respect to A fibered manifold together with a manifold is a fiber bundle with typical fiber (or just fiber) if it admits a local trivialization with respect to The atlas is then called a bundle atlas. See also Notes References Historical External links Differential geometry Fiber bundles Manifolds