Loop (topology)

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In mathematics, a loop in a topological space Template:Mvar is a continuous function Template:Mvar from the unit interval Template:Math to Template:Mvar such that Template:Nowrap In other words, it is a path whose initial point is equal to its terminal point.<ref name="ils">Template:Citation.</ref>

A loop may also be seen as a continuous map Template:Mvar from the pointed unit circle Template:Math into Template:Mvar, because Template:Math may be regarded as a quotient of Template:Mvar under the identification of 0 with 1.

The set of all loops in Template:Mvar forms a space called the loop space of Template:Mvar.<ref name="ils"/>

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