nLab
Brouwer's fixed point theorem

Contents

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

Brouwer‘s fixed point theorem says that every continuous function from a compact convex set to itself has at least one fixed point.

References

Textbook account

  • B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, corollary 15.3.4 of Modern Geometry — Methods and Applications: Part II: The Geometry and Topology of Manifolds, Graduate Texts in Mathematics 104, Springer-Verlag New York, 1985

See also

Discussion in cohesive homotopy type theory is in

Last revised on March 19, 2019 at 00:29:05. See the history of this page for a list of all contributions to it.