Theorem of Poincaré

The Poincaré theorem is a fundamental idea in topology stating that in a three-dimensional space resembling ordinary space, any closed, smooth surface without holes, like a sphere, is topologically the same as a standard sphere. More generally, it implies that a 3D space that is simply connected (no holes or tunnels) is equivalent to ordinary 3D space. Historically, the theorem was part of the effort to classify all possible shapes of the universe. Its proof was a major achievement in mathematics, confirming that our intuitive notions of space align with a rigorous mathematical understanding.