Related papers: Closure operators on dcpos

This work proposes an alternative approach to the so-called lattice of embedded subsets, which is included in the product of the subset and partition lattices of a finite set, and whose elements are pairs consisting of a subset and a…

There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the…

This paper examines operad structures derived from poset matrices by formulating a set of new construction rules for poset matrices. In this direction, eleven different partial composition operations will be introduced as the basis for the…

We show that a densely defined closable operator $A$ such that the resolvent set of $A^2$ is not empty is necessarily closed. This result is then extended to the case of a polynomial $p(A)$. We also generalize a recent result by…

Abstract Compared to existing schemes, the decomposition of moment tensors for mining-induced seismic events into closing-crack and double-couple components has the advantage that each can be interpreted in terms of a physical source…

We give conditions for a locally finite poset $P$ to have the property that for any functions $f:P\to {\bf C}$ and $g:P\to {\bf C}$ not identically zero and linked by the M\"obius inversion formula, the support of at least one of $f$ and…

We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…

Using the operators of taking upper and lower cones in a poset with a unary operation, we define operators M(x,y) and R(x,y) in the sense of multiplication and residuation, respectively, and we show that by using these operators, a general…

Let $G$ be an acylic directed graph. For each vertex $g \in G$, we define an involution on the independent sets of $G$. We call these involutions flips, and use them to define a new partial order on independent sets of $G$. Trim lattices…

We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…

In a previous paper, the authors introduced the idea of a symmetric pair of operators as a way to compute self-adjoint extensions of symmetric operators. In brief, a symmetric pair consists of two densely defined linear operators $A$ and…

The order topology $\tau_o(P)$ (resp. the sequential order topology $\tau_{os}(P)$) on a poset $P$ is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a…

We study the spectral properties of positive absolutely minimum attaining operators defined on infinite dimensional complex Hilbert spaces and using that derive a characterization theorem for such type of operators. We construct several…

Recently, in order to broad the application and theoretical areas of rough sets and matroids, some authors have combined them from many different viewpoints, such as circuits, rank function, spanning sets and so on. In this paper, we…

In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.

The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…

In this work we describe the mathematical foundations used in the construction of primary fields of minimal models of conformal field theory. The work contains two parts: In the first part we give a description of Verma and Fock modules for…

This paper investigates an iterative rank-one decomposition scheme for positive operators on a Hilbert space based on a residual-weighted congruence update. At each step the operator is compressed along a chosen unit vector while remaining…

In this paper, we introduce the notion of $\mathcal{M}$-convergence and $\mathcal{MN}$-convergence structures in posets, which, in some sense, generalise the well-known Scott-convergence and order-convergence structures. As results, we give…

This is the first paper in a series on intrinsic Donaldson-Thomas theory, where we develop a new framework for enumerative geometry that allows the generalization of constructions and results from linear moduli stacks to general non-linear…