The space $\Omega X$ of all loops (cf. Loop (in topology)) at the point $*$ in a topological space $X$ with distinguished point $*$, endowed with the compact-open topology. A loop space is a fibre in the Serre fibration $(E,p,X)$ over the space $X$ (here $E$ is the path space).
|[a1]||J.F. Adams, "Infinite loop spaces" , Princeton Univ. Press (1978)|
Loop space. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Loop_space&oldid=31872