generalized Cartesian product

Given any family of sets {Aj}jJ indexed by an index setMathworldPlanetmath J, the generalized Cartesian product


is the set of all functions


such that f(j)Aj for all jJ.

For each iJ, the projection map


is the function defined by


The generalized Cartesian product is the productPlanetmathPlanetmathPlanetmath ( in the category of sets.

The axiom of choiceMathworldPlanetmath is the statement that the generalized Cartesian product of nonempty sets is nonempty. The generalized Cartesian product is usually called the Cartesian productMathworldPlanetmath.

Title generalized Cartesian product
Canonical name GeneralizedCartesianProduct
Date of creation 2013-03-22 11:49:02
Last modified on 2013-03-22 11:49:02
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 15
Author Mathprof (13753)
Entry type Definition
Classification msc 03E20
Related topic CartesianProduct
Related topic ProductTopology
Related topic AxiomOfChoice
Related topic OrderedTuplet
Related topic FunctorCategory2
Defines projection map