Displaying similar documents to “Some examples of true F σ δ sets”

A remark on a theorem of Solecki

Petr Holický, Luděk Zajíček, Miroslav Zelený (2005)

Commentationes Mathematicae Universitatis Carolinae

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S. Solecki proved that if ℱ is a system of closed subsets of a complete separable metric space X , then each Suslin set S ⊂ X which cannot be covered by countably many members of ℱ contains a G δ set which cannot be covered by countably many members of ℱ . We show that the assumption of separability of X cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the σ -ideal generated by ℱ is locally determined. Using Solecki’s arguments, our result...

Densely continuous forms, pointwise topology and cardinal functions

Dušan Holý, Peter Vadovič (2008)

Czechoslovak Mathematical Journal

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We consider the space D ( X , Y ) of densely continuous forms introduced by Hammer and McCoy and investigated also by Holá . We show some additional properties of D ( X , Y ) and investigate the subspace D * ( X ) of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence τ p . The largest part of the paper is devoted to the study of various cardinal functions for ( D * ( X ) , τ p ) , in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, π -weight,...

An independency result in connectification theory

Alessandro Fedeli, Attilio Le Donne (1999)

Commentationes Mathematicae Universitatis Carolinae

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A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let ψ be the following statement: “a perfect T 3 -space X with no more than 2 𝔠 clopen subsets is connectifiable if and only if no proper nonempty clopen subset of X is feebly compact". In this note we show that neither ψ nor ¬ ψ is provable in ZFC.