Related papers: Variants on Digital Covering Maps
We study several types of multivalued functions in digital topology.
Maps have always been an essential component of autonomous driving. With the advancement of autonomous driving technology, both the representation and production process of maps have evolved substantially. The article categorizes the…
We introduce three generalizations of homotopy equivalence in digital images, to allow us to express whether a finite and an infinite digital image are similar with respect to homotopy. We show that these three generalizations are not…
The continuous evolution of cities poses significant challenges in terms of managing and understanding their complex dynamics. With the increasing demand for transparency and the growing availability of open urban data, it has become…
In the paper, we introduce the terminology equivariant pointwise clutching map. By using this, we give details on how to glue an equivariant vector bundle over a finite set so as to obtain a new Lie group representation such that the…
We present enumerations of a class of maps on Klein bottle which give rise to semi-equivelar maps. Semi-equivelar maps are generalizations of equivelar maps. There are eleven types of semi-equivelar maps on the Klein bottle. These are of…
In "Rips complexes and covers in the uniform category" \cite{Rips} the authors define, following James \cite{J}, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of…
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…
In this paper, we investigate several properties of the solution maps of variational inequalities with polynomial data. First, we prove some facts on the $R_0$-property, the local boundedness, and the upper semicontinuity of the solution…
Quantum Computing is a new paradigm that enables several advances which are impossible using classical technology. With the rise of quantum computers, the software is also invited to change so that it can better fit this new computation…
A subvariety of a complex projective space has a well-known dual variety, which is the set of its tangent hyperplanes. The purpose of this paper is to generalise this notion for a subvariety of a quite general partial flag variety. A…
This paper presents fifteen problems about mapping class groups. It is an expanded and updated version of the author's preprint "Ten problems on the mapping class groups". The paper will appear in the book "Problems on Mapping Class Groups…
A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on…
Hayman's conjecture about covering of vertical intervals under regular mappings is proved.
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the vertex set by cliques (clique covering…
We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper…
Generalized are the investigated in other works of the author transports along paths in fibre bundles to transports along arbitrary maps in them. Their structure and some properties are studied. Special attention is paid to the linear case…
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…
We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.