nLab
plane

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Manifolds and cobordisms

Contents

Definition

The plane is the Cartesian space 2\mathbb{R}^2. This is naturally a topological space, a manifold, and a smooth manifold.

This is the stage of Euclidean geometry.

References

For discussion of the plane via axioms for the points and lines in it (synthetic geometry) see the references at Euclidean geometry.

Revised on March 17, 2017 01:49:41 by Urs Schreiber (192.41.133.235)