Ultrafilters and Partial Products of Infinite Cyclic Groups

Ultrafilters and Partial Products of Infinite Cyclic Groups

We consider, for infinite cardinals κ and α ≤ κ+, the group Π(κ,<α) of sequences of integers, of length κ, with non-zero entries in fewer than α positions. Our main result tells when Π(κ,<α) can be embedded in Π(λ,<β). The proof involves some set-theoretic results, one about families of finite sets and one about families of ultrafilters. Partially supported by NSF grant DMS–0070723. Part of thi...

Purely infinite partial crossed products

Let (A, G, alpha) be a partial dynamical system. We show that there is a bijective corespondence between Ginvariant ideals of A and ideals in the partial crossed prroduct A xalpha, r G provided the action is exact and residually topologically free.

Generated topology on infinite sets by ultrafilters

Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.

Ultrafilters and Abelian Groups

on varietal capability of infinite direct products of groups

recently‎, ‎the authors gave some conditions under which a direct product‎ ‎of finitely many groups is $mathcal{v}-$capable if and only if each of its‎ ‎factors is $mathcal{v}-$capable for some varieties $mathcal{v}$‎. ‎in this paper‎, ‎we extend this fact to any infinite direct product of groups‎. ‎moreover‎, ‎we conclude some results for $mathcal{v}-$capability of direct products of infinitel...