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
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.