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Productively Lindelöf and indestructibly Lindelöf spaces. (English) Zbl 1284.54037

The paper is a continuation of the study of two important classes of Lindelöf spaces: productively Lindelöf (spaces whose product with any Lindelöf space is Lindelöf) and indestructible Lindelöf (spaces which remain Lindelöf in each countably closed forcing extension), and their relationships with selection principles and topological games. The authors also discuss an old, still open, question of Michael: if \(X\) is productively Lindelöf, is \(X^{\omega}\) Lindelöf? It is proved that under CH regular \(\aleph_1\)-Čech-complete, productively Lindelöf spaces \(X\) satisfy \(X^{\omega}\) is Lindelöf. Connections with projective properties are also considered. A topological property \(\mathcal P\) is projective if for each \(X\) with \(\mathcal P\), every continuous image of \(X\) onto a separable metrizable space also has \(\mathcal P\).

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54A35 Consistency and independence results in general topology
54B10 Product spaces in general topology
03E35 Consistency and independence results
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References:

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