Displaying similar documents to “Product properties for pairwise Lindelöf spaces.”

Lindelöf property and the iterated continuous function spaces

G. Sokolov (1993)

Fundamenta Mathematicae

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We give an example of a compact space X whose iterated continuous function spaces C p ( X ) , C p C p ( X ) , . . . are Lindelöf, but X is not a Corson compactum. This solves a problem of Gul’ko (Problem 1052 in [11]). We also provide a theorem concerning the Lindelöf property in the function spaces C p ( X ) on compact scattered spaces with the ω 1 th derived set empty, improving some earlier results of Pol [12] in this direction.

Vietoris topology on spaces dominated by second countable ones

Carlos Islas, Daniel Jardon (2015)

Open Mathematics

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For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = FK : K ∈ C(M) ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂ FL for any K;L ∈ C(M). A space X is strongly dominated by a space M if there exists an M-ordered compact cover F such that for any compact K ⊂ X there is F ∈ F such that K ⊂ F . Let K(X) D C(X){Øbe the set of all nonempty compact subsets...