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Adequate families of sets and Corson compacts. (English) Zbl 0586.54022
It is known that the space \(C_ p(X)\) is Lindelöf for every Corson compact X and if \(C_ p(Y)\) is a Lindelöf \(\Sigma\)-space (with a compact space Y) then Y is a Corson compact. With the use of the notions of a bush and an adequate family the author constructs a Corson compact X for which the space \(C_ p(X)\) fails to be a Lindelöf \(\Sigma\)-space. The construction of X depends on the existence of a Souslin tree and answers (in the negative) the question of A. V. Arkhangel’skij. The authors examined also the connections between the notions of an adequate family and Eberlein (Corson) compacts.
Reviewer: M.G.Tkachenko

MSC:
54C40 Algebraic properties of function spaces in general topology
54D30 Compactness
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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