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Loop (topology) : ウィキペディア英語版
Loop (topology)

A loop in mathematics, in a topological space ''X'' is a continuous function ''f'' from the unit interval ''I'' = () to ''X'' such that ''f''(0) = ''f''(1). In other words, it is a path whose initial point is equal to the terminal point.〔.〕
A loop may also be seen as a continuous map ''f'' from the unit circle ''S''1 into ''X'', because ''S''1 may be regarded as a quotient of ''I'' under the identification of 0 with 1.
The set of all loops in ''X'' forms a space called the loop space of ''X''.〔
==See also==

*Free loop
*Loop group
*Loop space
*Loop algebra
*Fundamental group
*Quasigroup

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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