Related papers: On scattered convex geometries
The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy…
The usual notion of set-convexity, valid in the classical Euclidean context, metamorphoses into several distinct convexity types in the more general Riemannian setting. By studying this phenomenon in reverse, we characterize complete…
The theory of bounded, distributive lattices provides the appropriate language for describing directionality and asymptotics in dynamical systems. For bounded, distributive lattices the general notion of `set-difference' taking values in a…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space $X$ with compact remainder (partially ordered by the standard partial…
We study the canonical weak distributive law $\delta$ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. For this subclass we characterise $\delta$ as a convex…
A left order on a magma (e.g., semigroup) is a total order of its elements that is left invariant under the magma operation. A natural topology can be introduced on the set of all left orders of an arbitrary magma. We prove that this…
Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including…
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…
In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S. We introduce the concept of exit edges, which…
A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this…
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Following ideas of A.C.Cochran, we give a suitable definition of a saturated uniformly A-convex algebra. In the m-convex case, such algebra is a uniform topological one.
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…
We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We initiate a study of the new theory of convex geometry and polytopes associated to polyptych lattices. In…
We prove that every pointed closed convex set in $\mathbb{R}^n$ is the intersection of all the rational closed halfspaces that contain it. This generalizes a previous result by the authors for compact convex sets.
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in…