Maximal almost disjoint families of functions
نویسندگان
چکیده
منابع مشابه
Mrówka Maximal Almost Disjoint Families for Uncountable Cardinals
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 numbersN . 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-ultrafilt...
متن کاملAnalytic and coanalytic families of almost disjoint functions
If F ⊆ N N is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable H ⊆ N N, no member of which is covered by finitely many functions from F , there is f ∈ F such that for all h ∈ H there are infinitely many integers k such that f (k) = h(k). However if V = L then there exists a coanalytic family of pairwise eventua...
متن کاملInvariance properties of almost disjoint families
We answer a question of Gracia-Ferreira and Hrušák by constructing consistently a MAD family maximal in the Katětov order. We also answer several questions of Garcia-Ferreira.
متن کاملA Special Class of Almost Disjoint Families
The collection of branches (maximal linearly ordered sets of nodes) of the tree ω (ordered by inclusion) forms an almost disjoint family (of sets of nodes). This family is not maximal – for example, any level of the tree is almost disjoint from all of the branches. How many sets must be added to the family of branches to make it maximal? This question leads to a series of definitions and result...
متن کاملAlmost disjoint families of connected sets
We investigate the question which (separable metrizable) spaces have a ‘large’ almost disjoint family of connected (and locally connected) sets. Every compact space of dimension at least 2 as well as all compact spaces containing an ‘uncountable star’ have such a family. Our results show that the situation for 1-dimensional compacta is unclear. 2004 Elsevier B.V. All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2009
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm204-3-3