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The space $E$ of the fibre space $(E,p,X)$, which is called the path fibre space. Here $X$ is a [[path-connected space]] with a distinguished point $*$, $E$ is the set of [[path]]s in $X$ starting from $*$ and $p$ is the mapping associating to each path its end-point. Moreover, $E$ is considered to have the compact-open topology. The fibre of this fibre space (which is a [[Serre fibration]]) is the [[Loop space|loop space]] $\Omega X$ — the set of all loops (cf. [[Loop (in topology)]]) in $X$ at $*$. A path space can be contracted within itself to a point, so the homotopy groups $\pi_n(E)=0$, and the homotopy sequence of the path fibre space degenerates into the so-called Hurewicz isomorphisms:

$$\pi_n(\Omega X)\approx\pi_{n+1}(X).$$



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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E.H. Spanier,   "Algebraic topology" , McGraw-Hill  (1966)  pp. 75ff, 99ff</TD></TR></table>