Orientability

Orientability is a concept in topology and differential geometry that refers to the property of a manifold regarding the consistent choice of direction or "orientation" across its entirety. A manifold is said to be orientable if it is possible to assign a consistent choice of orientation to all its tangent spaces. To illustrate this, consider the following examples: 1. **Orientable Manifold**: The surface of a sphere is an example of an orientable manifold.