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Kernel (set theory) : ウィキペディア英語版 | Kernel (set theory)
In set theory, the kernel of a function ''f'' may be taken to be either *the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function ''f'' can tell",〔.〕 or *the corresponding partition of the domain. ==Definition== For the formal definition, let ''X'' and ''Y'' be sets and let ''f'' be a function from ''X'' to ''Y''. Elements ''x''1 and ''x''2 of ''X'' are ''equivalent'' if ''f''(''x''1) and ''f''(''x''2) are equal, i.e. are the same element of ''Y''. The kernel of ''f'' is the equivalence relation thus defined.〔
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