 Homogeneous space

A homogeneous space is a space on which a group acts transitively. After choosing a point, a transitive Lie-group action identifies the space with a quotient $G/H$ by the point stabilizer.

A homogeneous space is a mathematical structure that exhibits a high degree of symmetry. More formally, in the context of geometry and algebra, a homogeneous space can be defined as follows: 1. **Definition**: A space \(X\) is called a homogeneous space if for any two points \(x, y \in X\), there exists a symmetry operation (usually described by a group action) that maps \(x\) to \(y\).