nLab
Jordan curve theorem

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

Contents

Idea

The Jordan curve theorem is a basic fact in topology. It stands out as having a statement that intuitively seems completely obvious, but which turns out to require a non-trivial formal proof.

The theorem states that every continuous loop (where a loop is a closed curve) in the Euclidean plane which does not intersect itself (a Jordan curve) divides the plane into two disjoint regions?, the inside contained in the curve, and the outside.

References

Revised on September 6, 2017 07:19:12 by Urs Schreiber (77.56.177.247)