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• W3015596151 abstract "For a Tychonoff space X and a family λ of subsets of X, we denote by Cλ(X) the T1-space of all real-valued continuous functions on X with the λ-open topology. A topological space is productively Lindelöf if its product with every Lindelöf space is Lindelöf. A space is indestructibly productively Lindelöf if it is productively Lindelöf in any extension by countably closed forcing. A Menger space is a topological space in which for every sequence of open covers U1,U2,... of the space there are finite sets F1⊂U1,F2⊂U2,... such that family F1∪F2∪... covers the space. In this paper, we study indestructibly productively Lindelöf and Menger function spaces. In particular, we proved that the following statements are equivalent for a T1-space Cλ(X): (1) Cλ(X) is indestructibly productively Lindelöf; (2) Cλ(X) is metrizable Menger; (3) Cλ(X) is metrizable σ-compact; (4) X is pseudocompact, D(X) is a dense C⁎-embedded set in X and the family λ consists of all finite subsets of D(X), where D(X) is the countable set of all isolated points of X; (5) Cλ(X) is homeomorphic to Cp⁎(N)." @default.
• W3015596151 created "2020-04-17" @default.
• W3015596151 creator A5034916596 @default.
• W3015596151 date "2020-08-01" @default.
• W3015596151 modified "2023-09-25" @default.
• W3015596151 title "Indestructibly productively Lindelöf and Menger function spaces" @default.
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• W3015596151 doi "https://doi.org/10.1016/j.topol.2020.107202" @default.
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