nLab
manifold with boundary

Idea

A manifold is a topological space that is locally isomorphic to a Cartesian space ${ℝ}^n$.

A manifold with boundary is a topological space that is locally isomorphic either to an ${ℝ}^n$ or to a half-space $H^n=\{\stackrel{\rightharpoonup }{x}\in {ℝ}^n\mid x^n\ge 0\}$.

A manifold with corners is a topological space that is locally isomorphic to an $H_i^n=\{\stackrel{\rightharpoonup }{x}\in {ℝ}^n\mid x^i,x^{i+1},\cdots ,x^n\ge 0\}$ for $0\le i\le n$.

For details see manifold.

Related concepts

• closed manifold

References

• Dominic Joyce, On manifolds with corners (arXiv:0910.3518)