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).
Comments
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
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