family of sets
A family of sets consists of an index set and, for each element of , a set .
Given , a set and a function , we get a family of sets by defining to be the preimage .
Conversely, given a family of sets, let be the disjoint union
and let be .
(We should talk about ways to formalise this concept in various forms of set theory and when the latter construction above requires the axiom of collection.)
Revised on January 15, 2011 06:00:41
by Toby Bartels