Abstract:We give sufficient and necessary conditions to be fulfilled by a filter $\Psi $ and an ideal $\Lambda $ in order that the $\Psi $-quotient space of the $\Lambda $-ideal product space preserves $T_k$-properties ($k=0,1,2,3,3\frac {1}{2}$) (``in the sense of the \L os theorem''). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.
Keywords: separation axioms, box product, ultraproduct, ideal product topology
AMS Subject Classification: Primary 54B10, 54D10, 54D15