On separatedness of reduced ideal-products (Q1369011)

The authors consider some very specialized separation properties for a somewhat general topological space. The space is a quotient space obtained from the ideal-product space that they call the reduced ideal-product space. Their concern is with the infinitude of separation axioms between the \(T_2\) and \(T_3\) axioms known as \(\alpha\)-separatedness, where \(\alpha \in On\). The major result shows that the reduced ideal-product preserves \(n\)-separatedness for each \(n \in \omega.\) Thus these properties are preserved in all interesting topological products such as Tychonoff, box, ultraproducts and the like.