Analytic manifold

An **analytic manifold** is a type of manifold that has a special structure allowing for the use of analytic functions in its local charts. It is a mathematical object that combines the concepts of topology and analysis. ### Definition: 1. **Topological Manifold**: An analytic manifold is first defined as a topological manifold, which means it is a topological space that resembles Euclidean space near each point.