# Cellular mapping

From Encyclopedia of Mathematics

A mapping from one relative CW-complex into another such that , where and are the -skeletons of and relative to and , respectively. In the case when , one obtains a cellular mapping from the CW-complex into the CW-complex .

A homotopy , where , is called cellular if for all . The following cellular approximation theorem is the analogue of the simplicial approximation theorem (see Simplicial mapping): Let be a mapping from one relative CW-complex into another the restriction of which to some subcomplex is cellular. Then there exists a cellular mapping that is homotopic to relative to .

For references see also CW-complex.

#### Comments

#### References

[a1] | E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) |

[a2] | R. Brown, "Elements of modern topology" , McGraw-Hill (1968) |

[a3] | C.R.F. Maunder, "Algebraic topology" , v. Nostrand (1970) pp. Section 7.5 |

**How to Cite This Entry:**

Cellular mapping. D.O. Baladze (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Cellular_mapping&oldid=12612

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098