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A closed [[path]]. In detail, a loop $f$ is a [[continuous mapping]] of the interval $[0,1]$ into a topological space $X$ such that $f(0) = f(1)$. The set of all loops in a space $X$ with a distinguished point $\star$ for which $f(0) = f(1) = {\star}$ forms the ''[[loop space]]'' $\Omega X$.

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How to Cite This Entry:
Loop (in topology). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Loop_(in_topology)&oldid=41992

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article

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