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Article

Levy, Ronnie ; Matveev, Mikhail
On monotone Lindelöfness of countable spaces. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 49 (2008), issue 1, pp. 155-161
MSC: 54D20 | MR 2433633 | Zbl 1212.54077
Keywords:
Lindelöf; monotonically Lindelöf; tower; the countable fan space; Pixley-Roy space
Summary:
A space is monotonically Lindelöf (mL) if one can assign to every open cover $\Cal U$ a countable open refinement $r(\Cal U)$ so that $r(\Cal U)$ refines $r(\Cal V)$ whenever $\Cal U$ refines $\Cal V$. We show that some countable spaces are not mL, and that, assuming CH, there are countable mL spaces that are not second countable.
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