Three-dimensional manifolds

Definition. A (topological) n-manifold M is a Hausdorff topological space with a countable basis of open sets, such that each point of M lies in an open set homeomorphic to R or R+ = {(x1, . . . , xn) ∈ R n : xn ≥ 0}. The boundary ∂M of M is the set of points not having neighbourhoods homeomorphic to R. The set M − ∂M is the interior of M , denoted int(M). If M is compact and ∂M = ∅, then M is closed.