集合族




在集合论和有关的数学分支中，给定集合S的子集的搜集F叫做S的子集族或S上的集合族。更一般的说，无论什么任何集合的搜集都叫做集合族。



例子




  • 幂集P(S)是在S上的集合族。

  • n元素集合S的k元素子集S(k)形成了集合族。

  • 所有序数的类Ord是“大”集合族；它自身不是集合而是真类。

  • 样本空间的某些子集组成的集合叫做集合族。



性质




  • S的任何子集族自身都是幂集P(S)的子集。

  • 不论什么集合族都是所有集合的真类（全集）V的子类。


  • 超图是集合V（顶点集合）加上V的非空子集族（边）。



参见















































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