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Keywords:
separation axioms; box product; ultraproduct; ideal product topology
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:
[1] Bankston P.: Ultraproducts in topology. Gen. Topology Appl. 7 (1977), 283-308. MR 0458351 | Zbl 0364.54005
[2] van Douwen E.K.: The box product of countably many metrizable spaces need not be normal. Fundamenta Mathematicae LXXXVIII.2 (1975), 127-132. MR 0385781
[3] Engelking R.: General Topology. PWN - Polish Scientific Publishers, 1977. MR 0500780 | Zbl 0684.54001
[4] Kelly J.L.: General Topology. Springer Verlag, Graduate Texts in Mathematics 27.
[5] Knight C.J.: Box topologies. Quart. J. Math. Oxford 15 (1964), 41-54. MR 0160184 | Zbl 0122.17404
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