Related papers: Cone monotone mappings: continuity and differentia…

We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…

Here we have introduced the idea of rough convergence of sequences in a cone metric space. Also it has been investigated how far several basic properties of rough convergence as valid in a normed linear space are affected in a cone metric…

We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the…

In this note, we study monotone dynamical systems with respect to polyhedral cones. Using the half-space representation and the vertex representation, we propose three equivalent conditions to certify monotonicity of a dynamical system with…

We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial.…

We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spaces, respectively. An order topology is introduced such that…

We provide a complete description of the tangent space of the cone of monotone plans in $\R\times \R$ with prescribed first projection. We show that elements of this tangent space are essentially made of two simple building-block types of…

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…

A wedge (i.e., a closed nonempty set in the Euclidean space stable under addition and multiplication with non-negative scalars) induces by a standard way a semi-order (a reflexive and transitive binary relation) in the space. The wedges…

For mappings in metric spaces satisfying one inequality with respect to modulus of families of curves, there is proved a lightness of the uniform limit of these mappings. It is proved that, the uniform limit of these mappings is light…

We introduce the notions of in-betweenness and monotonicity with respect to a metric, for operator means. These notions can be seen as generalising their natural counterpart for scalar means, and as a relaxation of the notion of geodesity.…

The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately…

We prove that the moduli space of stable maps of degree 2 to the moduli space of rank 2 stable bundles of fixed determinant O(-x) over a smooth projective curve of genus g>2 has two irre- ducible components which intersect transversely. One…

In this chapter we study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces,…

We give Ramsey expansions of classes of generalised metric spaces where distances come from a linearly ordered commutative monoid. This complements results of Conant about the extension property for partial automorphisms and extends an…

We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category…

We establish local characterizations of matrix monotonicity and convexity of fixed order by giving integral representations connecting the Loewner and Kraus matrices, previously known to characterize these properties, to respective Hankel…

We study notions of homotopy in the Newtonian space $N^{1,p}(X;Y)$ of Sobolev type maps between metric spaces. After studying the properties and relations of two different notions we prove a compactness result for sequences in homotopy…

A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is…