A property that is always fulfilled by the product of topological spaces, if it is fulfilled by each single factor. Examples of productive properties are connectedness,
and path-connectedness, axioms , , and , regularity and complete regularity, the property of being
a Tychonoff space, but not axiom and normality, which does not even pass, in general, from
a space
to .
Metrizability is not productive, but is preserved by products of at most spaces. Separability is not productive, but is preserved
by products of at most spaces.