Serre fibration

From Encyclopedia of Mathematics
Revision as of 17:12, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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


there is a mapping

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


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


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.


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