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- W2013111493 abstract "We consider generalizations of a well-known class of spaces, called by S. Mrówka, N∪R, where R is an infinite maximal almost disjoint family (MADF) of countable subsets of the natural numbers N. We denote these generalizations by ψ=ψ(κ,R) for κ⩾ω. Mrówka proved the interesting theorem that there exists an R such that |βψ(ω,R)∖ψ(ω,R)|=1. In other words there is a unique free z-ultrafilter p0 on the space ψ. We extend this result of Mrówka to uncountable cardinals. We show that for κ⩽c, Mrówka's MADF R can be used to produce a MADF M⊂[κ]ω such that |βψ(κ,M)∖ψ(κ,M)|=1. For κ>c, and every M⊂[κ]ω, it is always the case that |βψ(κ,M)∖ψ(κ,M)|≠1, yet there exists a special free z-ultrafilter p on ψ(κ,M) retaining some of the properties of p0. In particular both p and p0 have a clopen local base in βψ (although βψ(κ,M) need not be zero-dimensional). A result for κ>c, that does not apply to p0, is that for certain κ>c, p is a P-point in βψ." @default.
- W2013111493 created "2016-06-24" @default.
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- W2013111493 date "2010-06-01" @default.
- W2013111493 modified "2023-09-26" @default.
- W2013111493 title "Mrówka maximal almost disjoint families for uncountable cardinals" @default.
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- W2013111493 doi "https://doi.org/10.1016/j.topol.2009.08.024" @default.
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