 3-manifold

A three-manifold is a topological manifold locally modeled on ${\mathbb{R}}^3$, or on a half-space at its boundary.

A 3-manifold is a topological space that locally resembles Euclidean 3-dimensional space. More formally, a space \( M \) is called a 3-manifold if every point in \( M \) has a neighborhood that is homeomorphic (topologically equivalent) to an open subset of \( \mathbb{R}^3 \).