Editing Diffeology (section)

=== Products ===
If ''<math>X</math>'' and ''<math>Y</math>'' are diffeological spaces, then the '''product''' diffeology on the [[Cartesian product]] ''<math>X \times Y</math>'' is the diffeology generated by all products of plots of ''<math>X</math>'' and of ''<math>Y</math>''. Precisely, a map <math>p:U \to X \times Y</math> necessarily has the form <math>p(u) = (x(u),y(u))</math> for maps <math>x:U \to X</math> and <math>y:U \to Y</math>. The map <math>p</math> is a plot in the product diffeology if and only if <math>x</math> and <math>y</math> are plots of <math>X</math> and <math>Y</math>, respectively. This generalizes to products of arbitrary collections of spaces.

The D-topology of ''<math>X \times Y</math>'' is the coarsest delta-generated topology containing the [[product topology]] of the D-topologies of ''<math>X</math>'' and ''<math>Y</math>''; it is equal to the product topology when ''<math>X</math>'' or ''<math>Y</math>'' is [[locally compact]], but may be finer in general.<ref name="ChrSinWu14"/>