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Loop space

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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).


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References

[a1] J.F. Adams, "Infinite loop spaces" , Princeton Univ. Press (1978)
How to Cite This Entry:
Loop space. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Loop_space&oldid=31872
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article