Related papers: Sharp Elements and Apartness in Domains
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topological characterization of indecomposability which is new even in…
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. We will show that the D-completion of free algebras over a Scott space $\Sigma L$, on the context of directed spaces, are…
In this article, we study the relationship between notions of depth for sequences, namely, Bennett's notions of strong and weak depth, and deep $\Pi^0_1$ classes, introduced by the authors and motivated by previous work of Levin. For the…
Some notions in mathematics can be considered relative. Relative is a term used to denote when the variation in the position of an observer implies variation in properties or measures on the observed object. We know, from Skolem theorem,…
We study the computational complexity of fair division of indivisible items in an enriched model: there is an underlying graph on the set of items. And we have to allocate the items (i.e., the vertices of the graph) to a set of agents in…
We classify purely inseparable morphisms of degree $p$ between rational double points (RDPs) in characteristic $p > 0$. Using such morphisms, we refine a result of Artin that any RDP admits a finite smooth covering.
We define the finite extension property for $d$-dimensional subshifts, which generalizes the topological strong spatial mixing condition defined by Brice\~no (2016), and we prove that this property is invariant under topological conjugacy.…
In this study, the nonconforming finite elements of order two and order three are constructed and exploited for the Stokes problem. The moments of order up to $k-1$ ($k=2,3$) on all the facets of the tetrahedron are used for DoFs (degrees…
We present a notion of precompactness, and study some of its properties, in the context of apartness spaces whose apartness structure is not necessarily induced by any uniform one. The presentation lies entirely with a Bishop-style…
We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…
Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions represent computable…
In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type $\tto$ factors arising from countable discrete groups. We give simple criteria for…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
We consider various notions of completeness in symplectic topology and ask two related questions. Does a complete open symplectic manifold remain complete after excising a subset? Can two sets be made arbitrarily far apart by adjusting the…
A theorem of Mumford states that, on complex surfaces, any normal isolated singularity whose link is diffeomorphic to a sphere is actually a smooth point. While this property fails in higher dimensions, McLean asks whether the contact…
We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…
In this paper, we revisit Korn's inequality for the piecewise $H^1$ space based on general polygonal or polyhedral decompositions of the domain. Our Korn's inequality is expressed with minimal jump terms. These minimal jump terms are…