Closed manifold

A **closed manifold** is a type of manifold that is both compact and without boundary. More specifically, a manifold \( M \) is called closed if it satisfies the following conditions: 1. **Compact**: This means that the manifold is a bounded space that is also complete, meaning that every open cover of the manifold has a finite subcover. In simple terms, a compact manifold is one that is "finite" in a sense and can be covered by a finite number of open sets.