In
topology and related areas of
mathematics, a product space is the
cartesian product of a family of
topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more obvious topology called the
box topology, which can also be given to a product space and which agrees with the product topology when the product is over only finitely many spaces. However, the product topology is "correct" in that it makes the product space a
pullback of its factors, whereas the box topology is
too fine; this is the sense in which the product topology is "natural".
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