# 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:

Other references include:

• Tadayuki Haraguchi: On model structure for coreflective subcategories of a model category (2013-04-12T12:42:18Z): arXiv:1304.3622v1, MR3289294, Zbl 1311.55027.

• K. Shimakawa, K. Yoshida, T. Haraguchi: Homology and cohomology via enriched bifunctors (2010-10-16T10:31:57Z): arXiv:1010.3336v1.

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