# nLab Delta-generated space

### Context

#### Topology

topology

algebraic topology

# Contents

## Definition

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

## Properties

The category of $\Delta$-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

$\Delta$-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:

Revised on January 27, 2012 19:11:50 by Urs Schreiber (131.174.40.111)