Related papers: On Tarski's fixed point theorem
An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.
We study the lattice point problem associated with a special class of high-dimensional finite type domains via estimating the Fourier transforms of corresponding indicator functions.
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
We consider a model of two-sided matching market where buyers and sellers trade indivisible goods with the feature that each buyer has unit demand and seller has unit supply. The result of the existence of Walrasian equilibrium and lattice…
We present a new, category theoretic point of view on finite Ramsey theory. Our aims are as follows: -- to define the category theoretic notions needed for the development of finite Ramsey Theory, -- to state, in terms of these notions, the…
In this paper we give a new formulation of an abstract control problem in terms of a Grushin problem, so that we will reformulate all notions of controllability, observability and stability in a new form that gives readers an easy…
We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we prove various results of which the following is a prototype: If every diagram, indexed by…
It is shown that propositional intuitionistic logic is the maximal (with respect to expressive power) abstract logic satisfying a certain topological property reminiscent of compactness, the Tarski union property and preservation under…
A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In the contravariant case, the only such valuations are…
In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.
In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
The classification of lattice equations that are integrable in the sense of higher-dimensional consistency is extended by allowing directed edges. We find two cases that are not transformable via the 'admissible transformations' to the…
We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and…
The linguistic applications of the Lambek calculus suggest its semantics over algebras of formal languages. A straightforward approach to construct such semantics indeed yields a brilliant completeness theorem (Pentus 1995). However,…
The notion of unboundedly order converges has been recieved recently a particular attention by several authors. The main result of the present paper shows that the notion is efficient and deserves that care. It states that a vector lattice…
We give an analysis and generalizations of some long-established constructive completeness results in terms of categorical logic and pre-sheaf and sheaf semantics. The purpose is in no small part conceptual and organizational: from a few…
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at…
We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.