Related papers: Filters on a countable vector space
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
This paper deals with properties of filtrations on vector spaces indexed by partially ordered finitely generated abelian groups, which we call multifiltrations. We discuss the usual properties of filtrations, like exhaustivity and…
We investigate infinite versions of vector and affine space partition results, and thus obtain examples and a counterexample for a partition problem for relational structures. In particular we provide two (related) examples of an age…
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…
We define separating properties for normal ultrafilters. We prove that compactness and supercompactness are separable, yet compactness and measurability are not. We describe how to use separating properties in order to elicit distinct…
In this paper, we provide a combinatorial characterization of the elements of Schur ultrafilters on countable commutative groups. Using this characterization, we construct a free Schur ultrafilter on $\mathbb Z$ that is not infinitary…
Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable…
We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly…
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…
We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…
We continue investigations of reasonable ultrafilters on uncountable cardinals defined in Shelah math.LO/0407498 and studied also in math.LO/0605067. We introduce a general scheme of generating a filter on lambda from filters on smaller…
We study completeness of a topological vector space with respect to different filters on the set N of all naturals. In the metrizable case all these kinds of completeness are the same, but in non-metrizable case the situation changes. For…
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…
Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundamental properties and isolate some new ones, including a…
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Frechetness, strong Frechetness,…
For every filter $\mathcal F$ on $\mathbb N$, we introduce and study corresponding uniform $\mathcal F$-boundedness principles for locally convex topological vector spaces. These principles generalise the classical uniform boundedness…
Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these…