Additivity of the Gerlits--Nagy property and concentrated sets

Boaz Tsaban; Lyubomyr Zdomskyy

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arXiv · 1205.6824

Additivity of the Gerlits--Nagy property and concentrated sets

Boaz Tsaban·Lyubomyr Zdomskyy

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Abstract

We settle all problems posed by Scheepers, in his tribute paper to Gerlits, concerning the additivity of the Gerlits--Nagy property and related additivity numbers. We apply these results to compute the minimal number of concentrated sets of reals (in the sense of Besicovitch) whose union, when multiplied with a Gerlits--Nagy space, need not have Rothberger's property. We apply these methods to construct a large family of spaces, whose product with every Hurewicz space has Menger's property.

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Boaz Tsaban, Lyubomyr Zdomskyy. 2012-05-30. Additivity of the Gerlits--Nagy property and concentrated sets. https://arxiv.org/abs/1205.6824

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