Related papers: Neighboring mapping points theorem

In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of…

We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to…

We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that…

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems…

The present paper is devoted to the study of classes of mappings with non--bounded characteristics of quasiconformality. It is proved that the normal families of mappings distorting the families of mappings in ${\Bbb R}^n$ by special way,…

We prove a generalization of the classical Borsuk--Ulam Theorem under small perturbations (shaking) of the sphere. We show that for a generic perturbation of a continuous map $f : S^2 \to \mathbb{R}^2$, the number of points $x \in S^2$ such…

We introduce and study a new type of mappings in metric spaces termed $n$-point Kannan-type mappings. A fixed-point theorem is proved for these mappings. In general case such mappings are discontinuous in the domain but necessarily…

In this short note we study Bernstein's type theorem of translating solitons whose images of their Gauss maps are contained in compact subsets in an open hemisphere of the standard $\mathbf{S}^n$ (see Theorem 1.1). As a special case we get…

We extend Sharkovskii's theorem to the cases of $N$-dimensional maps which are close to 1D maps, with an attracting $n$-periodic orbit. We prove that, with relatively weak topological assumptions, there exist also $m$-periodic orbits for…

We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…

For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting…

We study algebraic varieties parametrized by topological spaces and enlarge the domains of Lawson homology and morphic cohomology to this category. We prove a Lawson suspension theorem and splitting theorem. A version of Friedlander-Lawson…

We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.

We describe the adjacency of vertices of the (unbounded version of the) set covering polyhedron, in a similar way to the description given by Chvatal for the stable set polytope. We find a sufficient condition for adjacency, and…

We describe a circle of ideas relating the dynamics of 2-dimensional homeomorphisms to that of 1-dimensional endomorphisms. This is used to introduce a new class of maps generalizing that of Thurston's pseudo-Anosov homeomorphisms.

An analysis of possible extension of the Painlev\'e test, to encompass the one-dimensional Vlasov equation, is performed. The extending requires a nontrivial generalization of the test. The proposed singularity analysis provides…

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…

Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of…

This paper establishes a Borsuk-Ulam type theorem for PL-manifolds with a finite group action, depending on the free equivariant cobordism class of a manifold. In particular, necessary and sufficient conditions are considered for a manifold…

In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to…