4-manifold

A 4-manifold is a topological space that locally resembles \(\mathbb{R}^4\) (four-dimensional Euclidean space) and is a type of manifold—a fundamental concept in topology and differential geometry. Formally, a 4-manifold \(M\) is a space that is Hausdorff, second countable, and locally homeomorphic to \(\mathbb{R}^4\).