3-manifolds

A **3-manifold** is a topological space that locally resembles Euclidean 3-dimensional space \(\mathbb{R}^3\). More formally, a 3-manifold is a Hausdorff space that is second-countable (any open cover has a countable subcover), and for every point in the manifold, there exists a neighborhood that is homeomorphic to an open subset of \(\mathbb{R}^3\).