nLab
product manifold

Contents

Contents

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.

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 08:47:38. See the history of this page for a list of all contributions to it.