相关论文: Exploring Topological Transitivity in Families of …

In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's…

We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…

The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical…

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extends the works of different authors…

There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…

Consider a continuous one parameter family of circles in complex plane that contains two circles lying in the exterior of one another. Under mild assumptions on the family, we prove that if a continuous function on the union of the above…

It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in…

In this paper, we prove some results in normal family of meromorphic mappings intersecting with moving hypersurfaces. As some applications, we establish some results for normal mapping and extension of holomorphic mappings. A our result is…

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…

Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such that all limit functions of G are non-constant. If for each f…

Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R,C) to give a new proof of classical Montel's theorem, about continuous solutions of Fr\'{e}chet's functional equation…

We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to…

In the present paper, we introduced the extended bicomplex plane $\bar{\mathbb{T}}$, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about the convergence of the sequences of…

We prove a Montel theorem for Hilbert space valued functions, and a non-commutative version of this theorem, by composing with unitaries to achieve convergence.

It is known that the topology of a Polish group is uniquely determined by its Borel structure and group operations, but this does not give us a way to find the topology. In this article we expand on this theorem and give a criterion for a…