nLab
Delta-generated space

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

A Δ\Delta-generated space is a topological space XX whose topology is the final topology induced by all maps Δ nX\Delta^n \to X, where Δ n\Delta^n runs over all the standard simplices.

Properties

The category of Δ\Delta-generated spaces is coreflective in Top. It is also locally presentable, and supports a model structure. Thus, it is a nice category of spaces.

References

Δ\Delta-generated spaces were originally proposed by Jeff Smith as a nice category of spaces for homotopy theory. A proof that they are locally presentable is in:

See also at directed homotopy theory.

Other references include:

Revised on July 30, 2015 18:43:51 by Urs Schreiber (195.113.30.252)