View source for Serre fibration

{{MSC|55}}
{{TEX|done}}

A triple $(X,p,Y)$, where $X$ and $Y$ are topological spaces and $p:X\to Y$ is a continuous mapping, with the following property (called the property of the existence of a
[[Covering homotopy|covering homotopy]] for polyhedra). For any finite polyhedron $K$ and for any mappings

$$f:K\times[0,1]\to Y, \qquad F_0:K=K\times\{0\}\to X$$
with

$$f\mid_{K\times\{0\}} = p\circ F_0$$
there is a mapping

$$F : K\times[0,1]\to X$$
such that $F\mid_{K\times\{0\}} = F_0$, $p\circ F=f$. It was introduced by J.-P. Serre in 1951 (see
{{Cite|Se}}).

====Comments====
A Serre fibration is also called a weak fibration. If the defining homotopy lifting property holds for every space (not just polyhedra), $p:X\to Y$ is called a fibration or Hurewicz fibre space.

====References====
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|valign="top"|{{Ref|Se}}||valign="top"|  J.P. Serre,   "Homologie singulière des espaces fibrés. Applications"  ''Ann. of Math.'', '''54'''  (1951)  pp. 425–505  {{MR|0045386}} {{MR|0039255}} {{MR|0039254}}  {{ZBL|0045.26003}} 

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|valign="top"|{{Ref|Sp}}||valign="top"|  E.H. Spanier,   "Algebraic topology", McGraw-Hill  (1966)  pp. Chapt. 2, §2; Chapt. 7, §2  {{MR|0210112}} {{MR|1325242}}  {{ZBL|0145.43303}} 

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