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Serre fibration

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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