Related papers: Generalizing a theorem of B\`{e}s and Choffrut

We generalize Hrushovski's Group Configuration Theorem to quasiminimal classes. As an application, we present Zariski-like structures, a generalization of Zariski geometries, and show that a group can be found there if the pregeometry…

We show that if $\mathbb{R} = A \cup B$ is a partition of $\mathbb{R}$ into two suborders $A$ and $B$, then there is an open interval $I$ such that $A \cap I$ is not order-isomorphic to $B \cap I$. The proof depends on the completeness of…

We show, under some natural conditions, that the set of abelian points on the non-anomalous subset of a closed irreducible subvariety $X$ intersected with the union of connected algebraic subgroups of codimension at least $\dim X$ in a…

In this note, we prove that the centralizer lattice ${\mathfrak C}(G)$ of a group $G$ cannot be written as a union of two proper intervals. In particular, it follows that ${\mathfrak C}(G)$ has no breaking point. As an application, we show…

This paper proves a general collapsing result for families of stratified Riemannian metrics $\widehat{g}^\mu$ on a compact orbifold $E$, subject to suitable limiting conditions on the metrics $\widehat{g}^\mu$ as $\mu \to \infty$. The…

Let $X$ be a very general hypersurface of degree $d$ in $\mathbb{P}^n$. We investigate positivity properties of the spaces $R_e(X)$ of degree $e$ rational curves in $X$. We show that for small $e$, $R_e(X)$ has no rational curves meeting…

In this paper, we investigate the general form of surjective (not necessarily linear) isometries T : A-> B between subspaces A and B of C(X;E) and C(Y;F), respectively.

By utilizing the idea of Colombeau's generalized function, we introduce a notion of asymptotic map between arbitrary diffeological spaces. The category consisting of diffeological spaces and asymptotic maps is enriched over the category of…

This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3…

Among other results, we prove the following theorem about Steiner minimal trees in $d$-dimensional Euclidean space: if two finite sets in $\mathbb{R}^d$ have unique and combinatorially equivalent Steiner minimal trees, then there is a…

We introduce a broader class of nonassociative Ore extensions that unifies and generalizes several earlier constructions. We prove generalizations of Hilbert's Basis Theorem for this class, showing that they arise immediately from the…

An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the…

In [O. Le Gal, J.-P. Rolin. An o-minimal structure which does not admit $C^\infty$ cellular decomposition. In: Ann. Inst. Fourier 59 (2009), pp 543-562], the authors construct an o-minimal structure which does not admit smooth…

This paper proves several natural generalizations of the theorem that for a generic, $C^k$ Riemannian metric on a smooth manifold, there are no closed, embedded, minimal submanifolds with nontrivial jacobi fields.

It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N…

The aim of this paper is to prove that there exists no cohomogeneity one $G-$invariant proper biharmonic hypersurface into the Euclidean space ${\mathbb R}^n$, where $G$ denotes a tranformation group which acts on ${\mathbb R}^n$ by…

In this paper we show that a convex subcomplex of a spherical building of type E6, E7 or E8 is a subbuilding or the automorphisms of the subcomplex fix a point on it. Together with previous results of M\"uhlherr-Tits, and Leeb and the…

In this paper we prove that for any definable subset $X\subset \mathbb{R}^{n}$ in a polynomially bounded o-minimal structure, with $dim(X)<n$, there is a finite set of regular projections (in the sense of Mostowski ). We give also a weak…

This work deals with undirected graphs that have the same betweenness centrality for each vertex, so-called betweenness uniform graphs (or BUGs). The class of these graphs is not trivial and its classification is still an open problem.…

We prove a sandwiching lemma for inner-exact locally compact Hausdorff \'etale groupoids. Our lemma says that every ideal of the reduced $C^*$-algebra of such a groupoid is sandwiched between the ideals associated to two uniquely defined…