Related papers: On a finite type Multivalued Shape
We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of…
We present some results related to theorems of Pasynkov and Torunczyk on the geometry of maps of finite dimensional compacta.
The aim of this paper is to refine and extend proposals by Sozeau and Tabareau and by Voevodsky for universe polymorphism in type theory. In those systems judgments can depend on explicit constraints between universe levels. We here present…
We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…
In this paper, we explore when a locally finite triangulated category has dimension zero or finite representation type. We also study generation of derived categories by orthogonal subcategories.
We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…
In this paper multivariate extension of the generalized Durrmeyer sampling type series are considered. We establish a Voronovskaja type formula and a quantitative version. Finally some particular examples are discussed.
The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of…
We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type. The paper covers the following topics: construction of integral models, their possible moduli…
We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples…
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is actually computable. Miller proved that finite-dimensional spheres have computable type, Iljazovi\'c and other authors established the property…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
For a certain class of compact oriented 3-manifolds, M. Goussarov and K. Habiro have conjectured that the information carried by finite-type invariants should be characterized in terms of ``cut-and-paste'' operations defined by the lower…
In this paper, Lusternik-Schinrelmann and geometric category of finite spaces are considered. We define new numerical invariants of these spaces derived from the geometric category and present an algorithmic approach for its effective…
This paper studies affine algebraic varieties parametrized by sine and cosine functions, generalizing algebraic Lissajous figures in the plane. We show that, up to a combinatorial factor, the degree of these varieties equals the volume of a…
We introduce and study a new family of extensions for the Borsuk-Ulam and topological Radon type theorems. The defining idea for this new family is to replace requirements of the form `a subset that is large in some sense goes to a…
The paper is devoted to one of the important notions of the shape theory: that of strong movability, which was primarily introduced by K. Borsuk for metrizable compacts. A strong movability criterion is proved for topological spaces, which…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
We develop the calculus of superforms as a tool for convex geometry. The formalism is applied to valuations on convex bodies, the Alexandrov-Fenchel inequalities and Monge- Amp\`ere equations on the boundary of convex bodies.