Related papers: Limiting Sets in Digital Topology
We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in…
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…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal and some are minimal with…
Digital nets (in base $2$) are the subsets of $[0,1]^d$ that contain the expected number of points in every not-too-small dyadic box. We construct sets that contain almost the expected number of points in every such box, but which are…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of…
Such modern applications of topology as data analysis and digital image analysis have to deal with noise and other uncertainty. In this environment, topological spaces often appear equipped with a real valued function. Persistence is a…
We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a…
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…
From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track…
In this paper, we study some properties of $*-$open and $*-$closed subsets of a space. The collection of all $*-$open subsets of a space $X$ form a topology on $X$ which is denoted by $^{*}O(X)$. We investigate the relations between…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
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…
We prove the existence of infinite dense free sets (in the usual topology) for set mappings on the reals, under reasonable assumptions.
An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set…
In this paper, we study some characterizations of fuzzifying strong compactness including nets and pre-subbases properties. We also introduve new characterizations of locally strong compactness in fuzzifying topology and mappings.