manifold with boundary

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

A **manifold with boundary** is a topological space that is locally isomorphic either to an $\mathbb{R}^n$ or to a **half-space** $H^n = \{ \vec x \in \mathbb{R}^n | x^n \geq 0\}$.

A **manifold with corners** is a topological space that is locally isomorphic to an $H^n_i = \{ \vec x \in \mathbb{R}^n | x^i , x^{i+1}, \cdots, x^n \geq 0\}$ for $0 \leq i \leq n$.

For details see manifold.

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

Discussion in the context of synthetic differential geometry realized in the Cahiers topos is in

- Vincent Schlegel,
*Gluing Manifolds in the Cahiers Topos*(arXiv:1503.07408)

Revised on April 29, 2015 20:02:59
by Urs Schreiber
(195.113.30.252)