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单词 induce
释义

induce

(induced) A structure on a mathematical object may naturally introduce a structure to subsets or related sets; that inherited structure is commonly referred to as ‘induced'. Likewise a function between sets might naturally give rise to or ‘induce' other functions between related sets.

For example, a metric on a set induces a metric on each subset and the topology on a set induces the subspace topology on a subset; a function between sets induces a function between their power sets; a continuous function between two spaces induces a homomorphism between their fundamental groups.

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更新时间:2025/4/29 15:53:09