nLab
manifold with boundary

Contents

Idea

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

A manifold with boundary is a topological space that is locally isomorphic either to an n\mathbb{R}^n or to a half-space H n={x n|x n0}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 i n={x n|x i,x i+1,,x n0}H^n_i = \{ \vec x \in \mathbb{R}^n | x^i , x^{i+1}, \cdots, x^n \geq 0\} for 0in0 \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)