Displaying similar documents to “Covering ω ω by special Cantor sets.”

Covering ω ω by special Cantor sets

Gary Gruenhage, Ronnie Levy (2002)

Commentationes Mathematicae Universitatis Carolinae

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This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω ω of irrationals, or certain of its subspaces. In particular, given f ∈ ω ( ω ∖ { 0 } ) , we consider compact sets of the form ∏ i ∈ ω B i , where | B i | = f ( i ) for all, or for infinitely many, i . We also consider “ n -splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω , | { g ( i ) : g ∈ K , g ↾ i = f ↾ i } | = n .

Around splitting and reaping

Jörg Brendle (1998)

Commentationes Mathematicae Universitatis Carolinae

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We prove several results on some cardinal invariants of the continuum which are closely related to either the splitting number 𝔰 or its dual, the reaping number 𝔯 .