nLab manifold with boundary

Context

Manifolds and cobordisms

manifolds and cobordisms

Contents

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 ${H}^{n}=\left\{\stackrel{⇀}{x}\in {ℝ}^{n}\mid {x}^{n}\ge 0\right\}$.

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

For details see manifold.

References

Revised on December 13, 2012 16:16:13 by Urs Schreiber (71.195.68.239)