Related papers: Equicontinuous mappings on finite trees

Given a dendrite $X$ and a continuous map $f\colon X\to X$, we show the following are equivalent: (i) $\omega_f$ is continuous and $\overline{\mathrm{Per}(f)}=\bigcap_{n\in\mathbb{N}}f^n(X)$; (ii) $\omega(x,f)=\Omega(x,f)$ for each $x\in…

For any composant $E \subset \mathbb H^*$ and corresponding near-coherence class $\mathscr E \subset \omega^*$ we prove the following are equivalent : (1) $E$ properly contains a dense semicontinuum. (2) Each countable subset of $E$ is…

Consider a Hausdorff space (X,T) and a set C of converging nets in X. By virtue of the limit uniqueness, the relation Lim which assigns each member x of X to every net N lying in C that converges to x is a map. Of course, structuring C with…

A singular foliation on a complete riemannian manifold M is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal,…

An ultrafilter $\mathcal{U}$ on a countable base {\em has continuous Tukey reductions} if whenever an ultrafilter $\mathcal{V}$ is Tukey reducible to $\mathcal{U}$, then every monotone cofinal map $f:\mathcal{U}\ra\mathcal{V}$ is continuous…

Let $X$ be a compact tree, $f$ be a continuous map from $X$ to itself, $End(X)$ be the number of endpoints and $Edg(X)$ be the number of edges of $X$. We show that if $n>1$ has no prime divisors less than $End(X)+1$ and $f$ has a cycle of…

Let $X$ be a compact metric countable space, let $f:X\to X$ be a homeomorphism and let $E(X,f)$ be its Ellis semigroup. Among other results we show that the following statements are equivalent: (i) $(X,f)$ is equicontinuous, (ii) $(X,f)$ is…

The behavior of a class of mappings of a domain of Euclidean space is studied. It is established that the indicated class is equicontinuous both at the inner and at the boundary points of the domain if the mappings contained in it satisfy…

The article is devoted to the study of mappings with finite distortion in metric spaces. Analogues of results relating to equicontinuity and normality of families of quasiregular mappings are obtained. It is proved that the indicated…

Let $f,g:X \to Y$ be continuous mappings. We say that $f$ is topologically equivalent to $g$ if there exist homeomorphisms $\Phi : X\to X$ and $\Psi: Y\to Y$ such that $\Psi\circ f\circ \Phi=g.$ Let $X,Y$ be complex smooth irreducible…

Given a selfmap $f:X\to X$ on a compact connected polyhedron $X$, H. Schirmer gave necessary and sufficient conditions for a nonempty closed subset $A$ to be the fixed point set of a map in the homotopy class of $f$. R. Brown and C.…

A continuum $X$ is a dendrite if it is locally connected and contains no simple closed curve, a self mapping $f$ of $X$ is called monotone if the preimage of any connected subset of $X$ is connected. If $X$ is a dendrite and $f:X\to X$ is a…

We call a function $f: X\to Y$ $P$-preserving if, for every subspace $A \subset X$ with property $P$, its image $f(A)$ also has property $P$. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural…

The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with discrete spectrum. To that end, we first determine when an isomorphic maximal equicontinuous factor map of…

In this paper, we introduce the notion of negatively regionally proximal pairs of onto maps which coincides with the set of regionally proximal pair of $f^{-1}$, whenever $f$ is an homeomorphism and we prove the maximal equicontinoues…

We study branching mappings that satisfy some condition of distortion of the modulus of families of paths. In a situation where the definition domain of mappings is locally connected on its boundary, the mapped domain is regular, and the…

We consider the following problem: Let $H$ and $F$ be two graphs on $k$ vertices and assume $F \neq H$. We say that $H$ and $F$ are incomparable if neither $F$ nor $H$ contains the other. Let $H$ be a graph on $k$ vertices and let $G$ be a…

There is a well-known correspondence between infinite trees and ultrametric spaces which can be interpreted as an equivalence of categories and comes from considering the end space of the tree. In this equivalence, uniformly continuous maps…

We give a necessary and sufficient condition for a map defined on a simply-connected quasiconvex metric space to factor through a tree. In case the target is the Euclidean plane and the map is H\"older continuous with exponent bigger than…

If $f:[a,b]\to \mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\mathbb{C}\to\mathbb{C}$ is map and $X$ is a continuum. We extend…