Search results for "Countable set"

ℓp-solutions of countable infinite systems of equations and applications to electrical circuits

1991

In the preceding chapter we have studied a lumped parameter model of a class of circuits containing a finite number of elements. Here we are interested in qualitative properties of the network in Figure 3.1.

Precise bounds for the sequential order of products of some Fréchet topologies

1998

Abstract The sequential order of a topological space is the least ordinal for which the corresponding iteration of the sequential closure is idempotent. Lower estimates for the sequential order of the product of two regular Frechet topologies and upper estimates for the sequential order of the product of two subtransverse topologies are given in terms of their fascicularity and sagittality. It is shown that for every countable ordinal α, there exists a Lasnev topology such that the sequential order of its square is equal to α.

Archimedean actions on median pretrees

2001

In this paper we consider group actions on generalized treelike structures (termed ‘pretrees’) defined simply in terms of betweenness relations. Using a result of Levitt, we show that if a countable group admits an archimedean action on a median pretree, then it admits an action by isometries on an [open face R]-tree. Thus the theory of isometric actions on [open face R]-trees may be extended to a more general setting where it merges naturally with the theory of right-orderable groups. This approach has application also to the study of convergence group actions on continua.

Vector-valued meromorphic functions

2002

A locally complete locally convex space E satisfies that every weakly meromorphic function defined on an open subset of \( \mathbb{C} \) with values in E is meromorphic if and only if E does not contain a countable product of copies of \( \mathbb{C} \). A characterization of locally complete spaces in the spirit of known characterizations of the (metric) convex compactness property is also given.

The branch set of a quasiregular mapping between metric manifolds

2016

Abstract In this note, we announce some new results on quantitative countable porosity of the branch set of a quasiregular mapping in very general metric spaces. As applications, we solve a recent conjecture of Fassler et al., an open problem of Heinonen–Rickman, and an open question of Heinonen–Semmes.

Countable recognizability of primitive periodic finitary linear groups

1997

Characterizing extreme points of polyhedra an extension of a result by Wolfgang Bühler

1982

This paper reconsiders the characterization given by Buhler admitting convex polyhedra of probability distributions on a finite or countable set which are given by systems of linear inequalities more complex than those considered before.

Generalized iterated function systems on the spacel∞(X)

2014

Abstract In the last decades there has been a current effort to extend the classical Hutchinson theory of iterated function systems composed by contractions on a metric space X into itself to more general spaces and infinitely many mappings. In this paper we consider the (countable) iterated function systems consisting of some generalized contractions on the product space X I into X , where I is an arbitrary set of natural numbers. Some approximations of the attractors of the respective iterated function systems are given.

The fractal interpolation for countable systems of data

2003

In this paper we will extend the fractal interpolation from the finite case to the case of countable sets of data. The main result is that, given an countable system of data in [a, b] ? Y, where [a, b] is a real interval and Y a compact and arcwise connected metric space, there exists a countable iterated function system whose attractor is the graph of a fractal interpolation function.

Nonlinear embeddings: Applications to analysis, fractals and polynomial root finding

2016

We introduce $\mathcal{B}_{\kappa}$-embeddings, nonlinear mathematical structures that connect, through smooth paths parameterized by $\kappa$, a finite or denumerable set of objects at $\kappa=0$ (e.g. numbers, functions, vectors, coefficients of a generating function...) to their ordinary sum at $\kappa \to \infty$. We show that $\mathcal{B}_{\kappa}$-embeddings can be used to design nonlinear irreversible processes through this connection. A number of examples of increasing complexity are worked out to illustrate the possibilities uncovered by this concept. These include not only smooth functions but also fractals on the real line and on the complex plane. As an application, we use $\mat…