Closed Manifold

A closed manifold is a mathematical shape that is finite and “without edges” or boundaries—think of it like the surface of a sphere or a donut. It smoothly encloses a space, meaning you can move around inside it without ever encountering a boundary or end. These shapes are studied in geometry and topology to understand their properties, such as curvature or holes. In essence, closed manifolds are complete, boundaryless spaces that can exist in any number of dimensions, offering a framework to analyze complex shapes that are self-contained and continuous.