Related papers: Dense free sets
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.
We prove that the outer automorphism group $\mathrm{Out}(N)$ of an infinitely generated free nilpotent group $N$ of class two is complete.
Most of the examples of wavelet sets are for dilation sets which are groups. We find a necessary and sufficient condition under which subspace wavelet sets exist for dilation sets of the form $A B$, which are not necessarily groups. We…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
We prove that the topological cycles of an arbitrary infinite graph induce a matroid. This matroid in general is neither finitary nor cofinitary.
We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the best known upper bound for the gaps in the sequence of…
We prove that if E a subset of an n-dimensional manifold, then every continuous R^n-valued map on E that is zero-free on the interior of E can be approximated in the fine topology, and hence, in particular, in the uniform topology, by a…
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
Free Steiner triple systems (STS) are infinite structures that are naturally characterised by a universal property. We consider the class of free STSs from a model theoretic viewpoint. We show that free STSs on any number of generators are…
A topological group $G$ is topologically normally generated if there exists $g \in G$ such that the normal closure of $g$ is dense in $G$. Let $S$ be a tame, infinite type surface whose mapping class group $\mathrm{Map}(S)$ is generated by…
We show that the set of entries generated by any finite set of doubly stochastic matrices is nowhere dense, in contrast to the cases of stochastic matrices or unitary matrices. In other words, there is no finite universal set of doubly…
We describe all finite subsemigroups of a free left regular band of infinite rank. Moreover, we show applications of this result in algebraic geometry and model theory.
We prove that for any infinite countable amenable group $G$, any $\epsilon > 0$ and any finite subset $K\subset G$, there exists a tiling (partition of $G$ into finite "tiles" using only finitely many "shapes"), where all the tiles are $(K;…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
We start by presenting a theory of finite sets using the approach which is essentially that taken by Whitehead and Russell in Principia Mathematica}, and which does not involve the natural numbers (or any other infinite set). This theory is…
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…
This paper grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or trivial first homology group. With this motivation we define a new class of groups. These…