# Serre fibration

From Encyclopedia of Mathematics

A triple , where and are topological spaces and is a continuous mapping, with the following property (called the property of the existence of a covering homotopy for polyhedra). For any finite polyhedron and for any mappings

with

there is a mapping

such that , . It was introduced by J.-P. Serre in 1951 (see [1]).

#### References

[1] | J.P. Serre, "Homologie singulière des espaces fibrés. Applications" Ann. of Math. , 54 (1951) pp. 425–505 |

#### Comments

A Serre fibration is also called a weak fibration. If the defining homotopy lifting property holds for every space (not just polyhedra), is called a fibration or Hurewicz fibre space.

#### References

[a1] | E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. Chapt. 2, §2; Chapt. 7, §2 |

**How to Cite This Entry:**

Serre fibration.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Serre_fibration&oldid=15485

This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article