Related papers: Digital topological groups
In this article, we investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between NP$_1$ and NP$_2$ product adjacencies.…
We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways…
With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as…
In this paper, we examine the relations of two closely related concepts, the digital Lusternik-Schnirelmann category and the digital higher topological complexity, with each other in digital images. For some certain digital images, we…
It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…
Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
In the literature of a digital-topological ($DT$-, for brevity) group structure on a digital image $(X,k)$, roughly saying, two kinds of methods are shown. Given a digital image $(X,k)$, the first one, named by a $DT$-$k$-group, was…
In previous work, we have defined---intrinsically, entirely within the digital setting---a fundamental group for digital images. Here, we show that this group is isomorphic to the edge group of the clique complex of the digital image…
The topology of digital images has been studied much in recent years, but no attempt has been made to exhaustively catalog the structure of binary images of small numbers of points. We produce enumerations of several classes of digital…
In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we present digital Hurewicz theorem for the fundamental group of digital images. We also…
In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…
D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy…
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…
We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms. We show that with appropriate topologies each class of these…
Digital topology has its own working conditions and sometimes differs from the normal topology. In the area of topological robotics, we have important counterexamples in this study to emphasize this red line between a digital image and a…
Topological full groups originated from the theory of topological dynamical systems and have been having considerable impact on group theory in recent years. This text represents an introduction/survey on topological full groups. After…
We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second homotopy group from algebraic topology. We illustrate that our…
For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain…