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 ).
|||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|
Serre fibration. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Serre_fibration&oldid=15485