Related papers: Coverings by open cells
In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of $n$ definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the…
Given an inverse semigroup $G_0$ of bounded type, we show, along with some other assumptions, that if the set of incompressible elements of $G_0$ is finite, then any finitely generated subgroup $G$ of the topological full group…
We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.
We prove a finiteness theorem for subgroups of bounded rank in hyperbolic $3$-manifold groups. As a consequence, we show that every bounded rank covering tower of closed hyperbolic $3$-manifolds is a tower of finite covers associated to a…
In this paper we work in an arbitrary o-minimal structure with definable Skolem functions and we prove that definably connected, locally definable manifolds are uniformly definably path connected, have an admissible cover by definably…
We prove that partially ordered set has finite number of finite-dimensional indecomposable nonequivalent Hilbert representations with orthoscalarity condition if and anly if it has finite number of indecomposable linear representations. We…
We prove that any ordered field can be extended to one for which every decreasing sequence of bounded closed intervals, of any length, has a nonempty intersection; equivalently, there are no Dedekind cuts with equal cofinality from both…
We consider a global semianalytic set defined by real analytic functions definable in an o-minimal structure. When the o-minimal structure is polynomially bounded, we show that the closure of this set is a global semianalytic set defined by…
A visceral structure on M is given by a definable base for a uniform topology on its universe in which all basic open sets are infinite and any infinite definable subset X of M has non-empty interior. This context includes o-minimal ordered…
We give a short and self-contained proof of the Marker-Steinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.
We prove that all linear Lie groups satisfying the conditions listed in the title are finite extensions of commutative Lie groups.
We analyse domination between invariant types in o-minimal expansions of ordered groups, showing that the domination poset decomposes as the direct product of two posets: the domination poset of an o-minimal expansion of a real closed…
In this paper, we introduce the notion of the universe, induced communities, and cells with their corresponding spots. Using this language, we formulate and prove the union close set conjecture by showing that for any finite universe…
The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open…
Let O be a compact orientable 3-orbifold with non-empty singular locus and a finite volume hyperbolic structure. (Equivalently, O is the quotient of hyperbolic 3-space by a lattice in PSL(2,C) with torsion.) Then we prove that O has a tower…
For a given d-minimal expansion $\mathfrak R$ of the ordered real field, we consider the expansion $\mathfrak R^\natural$ of $\mathfrak R$ generated by the sets of the form $\bigcup_{S \in \mathcal C}S$, where $\mathcal C$ is a subfamily of…
We prove that every orientable infinite type surface without boundary and finite genus has a Riemann surface structure such that its modular group of quasiconformal homeomorphisms is countable.
We show that a free action $G \curvearrowright X$ is almost finite if its restriction to some infinite normal subgroup of $G$ is almost finite. Consider the class of groups which contains all infinite groups of locally subexponential growth…
Finite covers are a technique for building new structures from simpler ones. The original motivation to study finite covers is in the Ladder theorem of Zilber which describes how totally categorical structures are built from strictly…
We consider d-minimal expansions of ordered fields. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied…