Related papers: Limiting Sets for Digital Cones and Suspensions
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.
Recently many papers on cone metric spaces have been appeared, and main topological properties of such spaces have been obtained. A cone metric space is Hausdorff, and first countable, so the topology of it coincides with a topology induced…
Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…
A point of a digital space is called simple if it can be deleted from the space without altering topology. This paper introduces the notion simple set of points of a digital space. The definition is based on contractible spaces and…
Properties of two classes of generally convex sets in the n-dimentional real Euclidean space, called m-semiconvex and weakly m-semiconvex, 1<=m<n, are investigated in the present work. In particular, it is established that an open set with…
The topic of fixed points in digital metric spaces has drawn yet more publications with assertions that are incorrect, incorrectly proven, trivial, or incoherently stated. We discuss publications with bad assertions concerning fixed points…
We introduce so-called cone topologies of paratopological groups, which are a wide way to construct counterexamples, especially of examples of compact-like paratopological groups with discontinuous inversion. We found a simple interplay…
In this paper we give some basic results on blocking sets on minimum size for a finite chain geometry.
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
The use of satellite networks has increased significantly in recent years due to their advantages over purely terrestrial systems, such as higher availability and coverage. However, to effectively provide these services, satellite networks…
Selectional restrictions are semantic constraints on forming certain complex types in natural language. The paper gives an overview of modeling selectional restrictions in a relational type system with morphological and syntactic types. We…
In this paper we consider the structure of $\omega$-limit sets in subshifts of Baire space. We consider both subshifts of finite type and subshifts of bounded type and we demonstrate that many classical structure theorems for $\omega$-limit…
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…
General definitions for causal structures on manifolds of dimension d+1>2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or…
We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ideals. Using efficient algorithms for constructing a…
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…
Topological semimetals have emerged as an important class of quantum materials with novel electronic responses and unconventional transport phenomena. Among them, nodal-line semimetals are distinguished by band crossings that extend along…
We show that the following properties are preserved under inverse limits: countable fan-tightness, q+, discrete generation and selective separability. We also present several examples based on inverse limits of countable spaces.