Manifolds

A manifold is a mathematical space that, in a small neighborhood around each point, resembles Euclidean space. Manifolds allow for the generalization of concepts from calculus and geometry to more abstract settings. ### Key Characteristics of Manifolds: 1. **Locally Euclidean**: Each point in a manifold has a neighborhood that is homeomorphic (topologically equivalent) to an open subset of Euclidean space \( \mathbb{R}^n \).