Lindelöf Spaces Which Are Menger, Hurewicz, Alster, Productive, or D
نویسنده
چکیده
We discuss relationships in Lindelöf spaces among the properties “Menger”, “Hurewicz”, “Alster”, “productive”, and “D”. This note is a continuation of [13]. The question of what additional assumptions ensure that the product of two Lindelöf spaces is Lindelöf is natural and well-studied. See e.g., [28], [30], [2], [3], [4], [5], [6], [32], [33]. D-spaces were introduced in [20]. Definition. A space X is D if for every neighbourhood assignment {Vx}x∈X , i.e. each Vx is an open set containing x, there is a closed discrete Y ⊆ X such that {Vx}x∈Y covers X. Y is called a kernel of the neighbourhood assignment. Research supported by grant A-7354 of the Natural Sciences and Engineering Research Council of Canada. (2000) Mathematics Subject Classification. Primary 54D45, 54D20, 54D99, 54A35, 03E35; Secondary 54G20, 54H05, 03E15, 03E17.
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