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单词 Fundamental Group
释义

Fundamental Group

The fundamental group of a Connected Set is the Quotient Group of the Group of all paths with initialand final points at a given point and the Subgroup of all paths Homotopic to thedegenerate path consisting of the point .


The fundamental group of the Circle is the Infinite Cyclic Group. Two fundamental groups having differentpoints are Isomorphic. If the fundamental group consists only of the identity element, thenthe set is Simply Connected.

See also Milnor's Theorem
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更新时间:2025/4/5 15:20:59