# Loop space

From Encyclopedia of Mathematics

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://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