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  "body": "\n## Definition\n\nLet $E$ and $B$ be [[topological spaces|0CQHFPGJ45]] and let $p \\colon E \\to B$ be a [[continuous map|0X3WGX95FE]].\nLet $I = [0, 1]$.\nThe map $p$ is a *Serre fibration* if it has the [[homotopy lifting property|G4QDM01P6J]] with respect to the cube $I^n$ for every integer $n \\ge 0$.\nThat is, let $n \\ge 0$, let $\\tilde f \\colon I^n \\to E$ be continuous, and let $H \\colon I^n \\times I \\to B$ be continuous with $H(x, 0) = p(\\tilde f(x))$ for all $x$.\nThen there is a continuous $\\tilde H \\colon I^n \\times I \\to E$ with $p \\circ \\tilde H = H$ and $\\tilde H(x, 0) = \\tilde f(x)$ for all $x \\in I^n$.\n\n## Remarks\n\nExample: for spaces $B$ and $F$, the projection $p \\colon B \\times F \\to B$ is a Serre fibration.\nGiven $\\tilde f = (f_1, f_2)$ and $H$, the map $\\tilde H(x, t) = (H(x, t), f_2(x))$ is a lift with the right start.\n\nNon-example: the inclusion $p \\colon \\set{0} \\to [0, 1]$ is not a Serre fibration.\nTake $n = 0$, $\\tilde f$ the map to $0$ and $H(t) = t$; any lift would satisfy $p(\\tilde H(1)) = 1$, but the only point of $\\set{0}$ maps to $0$.\n\nEquivalently, $p$ has the homotopy lifting property with respect to all CW complexes.\nEvery [[Hurewicz fibration|Y773B7EQA7]] is a Serre fibration, and every [[fiber bundle|CX4M8K61AB]] is a Serre fibration.\n",
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