nLab product manifold

Contents

Contents

1. Idea

Given two manifolds XX, YY (e.g. topological manifolds, differentiable manifolds, smooth manifolds, etc.) the product manifold X×YX \times Y is the Cartesian product in the corresponding category of manifolds: its underlying topological space is the product topological space and its charts are the Cartesian product of the given charts of XX and YY.

2. Examples

For Cartesian spaces we have

n 1× n 2 n 1+n 2\mathbb{R}^{n_1} \times \mathbb{R}^{n_2} \simeq \mathbb{R}^{n_1 + n_2}

Created on January 13, 2020 at 13:47:38. See the history of this page for a list of all contributions to it.