# Article

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Keywords:
separation axioms; box product; ultraproduct; ideal product topology
Summary:
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.
References:
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