Difference between revisions of "Loop space"
From Encyclopedia of Mathematics
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| + | The space $\Omega X$ of all loops (cf. [[Loop (in topology)|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|Serre fibration]] $(E,p,X)$ over the space $X$ (here $E$ is the [[Path space|path space]]). | ||
Latest revision as of 16:00, 19 April 2014
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