Products of H-separable spaces in the Laver model

Repovš, Dušan; Zdomskyy, Lyubomyr

doi:10.1016/j.topol.2018.02.021

Cited by 2 publications

(3 citation statements)

References 13 publications

(18 reference statements)

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“…More precisely, this is the case in the classical Laver model introduced in [14]. This improved an earlier result from [19] stating that in the same model, the product of any two countable H-separable spaces is M-separable. Consequently, in the Laver model the product of any two H-separable spaces is mH-separable provided that it is hereditarily separable.…”

Section: R-sepsupporting

confidence: 57%

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On regular separable countably compact ℝ-rigid spaces

Bardyla

Zdomskyy

2022

Isr. J. Math.

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In this paper we study the behaviour of selective separability properties in the class of Frechét-Urysohn spaces. We present two examples, the first one given in ZFC proves the existence of a countable Frechét-Urysohn (hence R-separable and selectively separable) space which is not H-separable; assuming p = c, we construct such an example which is also zero-dimensional and α 4 . Also, motivated by a result of Barman and Dow stating that the product of two countable Frechét-Urysohn spaces is Mseparable under PFA, we show that the MA is not sufficient here. In the last section we prove that in the Laver model, the product of any two H-separable spaces is mH-separable.

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Section: R-sepsupporting

confidence: 57%

“…The proof of the following statement is close to that of [19,Lemma 2.2], the only difference being a more careful analysis of sets of the form {n : R(U)(n) ⊂ U}. Proposition 5.2.…”

Section: Products Of H-separable Spaces In the Laver Modelmentioning

confidence: 68%