Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups
نویسندگان
چکیده
We study, from a set-theoretic point of view, those subgroups of the infinite direct product Z0 for which all homomorphisms to Z annihilate all but finitely many of the standard unit vectors. Specifically, we relate the smallest possible size of such a subgroup to several of the standard cardinal characteristics of the continuum. We also study some related properties and cardinals, both group-theoretic and set-theoretic. One of the set-theoretic properties and the associated cardinal are combinatorially natural, independently of any connection with algebra.
منابع مشابه
On Σ-countably Tight Spaces
Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality c if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and σ-countably tight compactum has cardinality c remains open. We also show that if an arbitrary product is σ-countably tight then all but finitel...
متن کاملAddendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...
متن کاملForcing Minimal Extensions of Boolean Algebras
We employ a forcing approach to extending Boolean algebras. A link between some forcings and some cardinal functions on Boolean algebras is found and exploited. We find the following applications: 1) We make Fedorchuk’s method more flexible, obtaining, for every cardinal λ of uncountable cofinality, a consistent example of a Boolean algebra Aλ whose every infinite homomorphic image is of cardin...
متن کاملType Ii∞ Factors Generated by Purely Infinite Simple C*-algebras Associated with Free Groups
Let Γ = G1 ∗G2 ∗ ... ∗Gn ∗ ... be a free product of at least two but at most countably many cyclic groups. With each such group Γ we associate a family of C*-algebras, denoted C∗ r (Γ,PΛ) and generated by the reduced group C*-algebra C∗ r Γ and a collection PΛ of projections onto the `2-spaces over certain subsets of Γ. We determine W ∗(Γ,PΛ), the weak closure of C∗ r (Γ,PΛ) in L(`2(Γ)), and us...
متن کاملOn the Product of Homogeneous Spaces*
Within the class of Tychonoff spaces, and within the class of topological groups, most of the natural questions concerning ‘productive closure’ of the subclasses of countably compact and pseudocompact spaces are answered by the following three well-known results: (1) [ZFC] There is a countably compact Tychonoff space X such that X XX is not pseudocompact; (2) [ZFC] The product of any set of pse...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994