Lindelöf spaces which are indestructible, productive, or D

Aurichi, Leandro F.; Tall, Franklin D.

doi:10.1016/j.topol.2011.09.039

Cited by 23 publications

(38 citation statements)

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“…The remainder of this paragraph assumes that d = ℵ 1 . Aurichi and Tall [3] improved several earlier results by proving that every productively Lindelöf space is Hurewicz. It was later shown that every productively Lindelöf space is productively Hurewicz and productively Menger [18,Theorem 8.2].…”

Section: Filter-menger Spacesmentioning

confidence: 73%

Products of Menger spaces: A combinatorial approach

Szewczak

Tsaban

2017

Annals of Pure and Applied Logic

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We construct Menger subsets of the real line whose product is not Menger in the plane. In contrast to earlier constructions, our approach is purely combinatorial. The set theoretic hypothesis used in our construction is far milder than earlier ones, and holds in all but the most exotic models of real set theory. On the other hand, we establish productive properties for versions of Menger's property parameterized by filters and semifilters. In particular, the Continuum Hypothesis implies that every productively Menger set of real numbers is productively Hurewicz, and each ultrafilter version of Menger's property is strictly between Menger's and Hurewicz's classic properties. We include a number of open problems emerging from this study.

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