# nLab CW approximation

## Theorems

#### Topology

topology

algebraic topology

# Contents

## Idea

For every topological space $X$ there is a CW complex $Z$ and a weak homotopy equivalence $f :Z\to X$. Such a map $f :Z\to X$ is called a CW approximation to $X$.

This is the notion of cofibrant replacement in the standard model structure on topological spaces.

## References

Revised on September 4, 2012 14:01:47 by Urs Schreiber (131.174.190.104)