Related papers: Extension dimension and refinable maps
We study the problem of extending an order-preserving real-valued Lipschitz map defined on a subset of a partially ordered metric space without increasing its Lipschitz constant and preserving its monotonicity. We show that a certain type…
We show that expansive maps from a dense subset of a compact metric space into the metric space itself are isometries
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…
A densely-defined symmetric linear map from/to a real Hilbert space extends to a self-adjoint map. Extension is expressed via Riesz representation. For a case including Friedrichs extension of a strongly monotone map, self-adjoint extension…
A variety of possible extensions of mappings between posets to their Dedekind order completion is presented. One of such extensions has recently been used for solving large classes of nonlinear systems of partial differential equations with…
We prove that a meromorphic map defined on the complement of a compact subset of a three-dimensional Stein manifold M and with values in a compact complex three-fold X extends to the complement of a finite set of points. If X is simply…
We construct a class of metric spaces whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\omega+k$ for any $k\in\mathbb{N}$, where $\omega$ is the smallest infinite ordinal number and a metric…
In this paper, we examine holomorphic Segre preserving maps between the complexifications of real hypersurfaces in $\mathbb{C}^{n+1}$. In particular, we find several sufficient conditions ensuring that Segre transversality and total Segre…
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…
We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding…
In terms of dilatations, it is proved a series of criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between regular domains on the Riemann surfaces
For a large class of nonuniformly expanding maps of $\Bbb R^m$, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques…
In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex…
We present some results related to theorems of Pasynkov and Torunczyk on the geometry of maps of finite dimensional compacta.
In this paper we extend the definitions of mean dimension and metric mean di-mension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
A persistence module with $m$ discrete parameters is a diagram of vector spaces indexed by the poset $\mathbb{N}^m$. If we are only interested in the large scale behavior of such a diagram, then we can consider two diagrams equivalent if…
Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. For maps like multiplication by an integer modulo 1, such sets have full…