Displaying similar documents to “Generalized projections of Borel and analytic sets”

Very small sets

Haim Judah, Amiran Lior, Ireneusz Recław (1997)

Colloquium Mathematicae

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Forcing countable networks for spaces satisfying R ( X ω ) = ω

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (1996)

Commentationes Mathematicae Universitatis Carolinae

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We show that all finite powers of a Hausdorff space X do not contain uncountable weakly separated subspaces iff there is a c.c.c poset P such that in V P X is a countable union of 0 -dimensional subspaces of countable weight. We also show that this theorem is sharp in two different senses: (i) we cannot get rid of using generic extensions, (ii) we have to consider all finite powers of X .

On the preservation of separation axioms in products

Milan Z. Grulović, Miloš S. Kurilić (1992)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient and necessary conditions to be fulfilled by a filter Ψ and an ideal Λ in order that the Ψ -quotient space of the Λ -ideal product space preserves T k -properties ( k = 0 , 1 , 2 , 3 , 3 1 2 ) (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.