# 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 $\mathbb{R}^n$.

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.

## References

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

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