nLab polyhedron

Contents

This article is about polyhedra in algebraic topology. For polyhedra in convex geometry, see the article polytope.

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

Definition

Definition

A topological space XX is a polyhedron if it is homeomorphic to the geometric realization of a finite simplicial complex and hence has a triangulation.

Properties

Remark

The study of polyhedra has been one of the sources for methods and applications in algebraic topology, and it is often useful to go back to see the motivations and applications in the older sources. For instance, shape morphisms between polyhedral spaces are just homotopy classes of continuous maps so the Cech invariants of polyhedra coincide with their ordinary ‘standard’ invariants.

Literature

Among textbook accounts:

Last revised on October 27, 2021 at 09:42:46. See the history of this page for a list of all contributions to it.