Related papers: Equivalent Conditions for Digital Covering Maps

SE Han's paper [11] discusses several variants of digital covering maps. We show several equivalences among these variants and discuss shortcomings in Han's paper.

We investigate the properties of digital homotopy in the context of digital pictures $(X,\kappa,\bar \kappa)$, where $X\subsetneq \Z^n$ is a finite set, $\kappa$ is an adjacency relation on $X$, and $\bar \kappa$ is an adjacency relation on…

In this paper, by reviewing the concept of subcovering and semicovering maps, we extend the notion of subcovering map to subsemicovering map. We present some necessary or sufficient conditions for a local homeomorphism to be a…

It is well-known that a homomorphism p between topological groups K, G is a covering homomorphism if and only if p is an open epimorphism with discrete kernel. In this paper we generalize this fact, in precisely, we show that for a…

We study a natural generalization of covering projections defined in terms of unique lifting properties. A map $p:E\to X$ has the "continuous path-covering property" if all paths in $X$ lift uniquely and continuously (rel. basepoint) with…

In this paper, we establish a new criterion for covering maps between real algebraic varieties. Specifically, we prove that a quasi-finite, flat morphism with locally constant geometric fibers between varieties over a real closed field…

The $\lambda$-perfect maps, a generalization of perfect maps (continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some results regarding $\lambda$-perfect maps will be…

The notions of a local $(k_0,k_1)$-isomorphism and a weakly local $(k_0,k_1)$-isomorphism play crucial roles in developing a digital $(k_0,k_1)$-covering space and a pseudo-$(k_0,k_1)$-covering space, respectively. In relation to the study…

The aim of this paper is to generalize some of the properties and results regarding both the coincidence point set and the common fixed point set of any two digitally continuous maps to the case of several (more than two) digitally…

In this study, we improve the topological complexity computations on digital images with introducing the digital topological complexity computations of a surjective and digitally continuous map between digital images. We also reveal…

In this paper, by reviewing the concept of semicovering maps, we present some conditions under which a local homeomorphism becomes a semicovering map. We also obtain some conditions under which a local homeomorphism is a covering map.

We develop an abstract model for the dynamics of an exponential map $z\mapsto \exp(z)+\kappa$ on its set of escaping points and, as an analog of Boettcher's theorem for polynomials, show that every exponential map is conjugate, on a…

A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa. Assume that there is no inner model with a Woodin cardinal and that every set has a sharp. Let K be the core model. Assume that kappa is a countably closed…

We develop a combinatorial framework to study certain polyhedral maps which are higher-dimensional analogues of tropical covers between metric graphs. Under a mild combinatorial assumption, we show that a map satisfies the so-called…

Local properties of the fundamental group of a path-connected topological space can pose obstructions to the applicability of covering space theory. A generalized covering map is a generalization of the classical notion of covering map…

We prove that $i)$ if $\mathcal{A}$ is $\lambda $-accessible and it is axiomatizable in (finitary) coherent logic then $\lambda $-pure maps are strict monomorphisms and $ii)$ if there is a proper class of strongly compact cardinals and…

We add to our knowledge of the approximate fixed point property (AFPP) in digital topology. We show that a digital image that is a tree has the AFPP. Given two digital images (X, \kappa) and (Y, \lambda) that have the approximate fixed…

Let $M$ be a $2$-space form. Let $P$ be a convex polygon in $M$. For these polygons, we define (and justify) a curvature $\kappa_i$ at each vertex $A_i$ of the polygon and and prove the following Blaschke's type theorem: If $P$ is a convex…

A map $p:E\to X$ has the \emph{unique path lifting} property if every path in $X$, after a choice of an initial point, lifts uniquely to a path in $E$. We prove that if a group $G$ acts on an $\mathbb R$-tree $T$ such that the quotient map…

Dynamic maps that allow continuous map rotations, e.g., on mobile devices, encounter new issues unseen in static map labeling before. We study the following dynamic map labeling problem: The input is a static, labeled map, i.e., a set P of…