Rosenlicht's Theorem

Rosenlicht's Theorem states that for certain algebraic structures called "varieties" with a group action, there exists a way to uniquely distinguish most points using rational functions. Specifically, it guarantees a "quotient space" where each point corresponds to a group orbit, allowing us to classify points up to the symmetry given by the group. In essence, it provides a method to understand complex geometric objects by simplifying their structure through functions that capture their intrinsic symmetries, aiding in the study of algebraic geometry and group actions.