Results 1 to 10 of about 75 (63)
Topologies on Zn that Are Not Homeomorphic to the n-Dimensional Khalimsky Topological Space [PDF]
Mathematics, 2019 The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on
Sang-Eon Han +2 more
doaj +2 more sources
REMARKS ON HOMOTOPIES ASSOCIATED WITH KHALIMSKY TOPOLOGY
Honam Mathematical Journal, 2015 Several kinds of homotopies have been substantially used to study topological properties of digital spaces. The present paper, as a survey article, studies some recent results in the field of homotopy theory associated with Khalimsky topology. In particular, Khalimsky topological properties of digital products related to the establishment of the ...
Sang-Eon Han, Sik Lee
exaly +3 more sources
CATEGORY WHICH IS SUITABLE FOR STUDYING KHALIMSKY TOPOLOGICAL SPACES WITH DIGITAL CONNECTIVITY [PDF]
Honam Mathematical Journal, 2011 Let X(η,k) be a Khalimsky topological n dimensionalsubspace with digital k-connectivity. In relation to the classica-tion of spaces X(η,k), by comparing several kinds of continuities andhomeomorphisms, the paper proposes a category which is suitablefor studying the spaces X(η,k).
Sang-Eon Han, Han Sang-Eon
exaly +2 more sources
AIMS Mathematics, 2021 <abstract><p>The present paper intensively studies various properties of certain topologies on the set of integers $ {\mathbb Z} $ (resp. $ {\mathbb Z}^n $) which are either homeomorphic or not homeomorphic to the typical Khalimsky line topology (resp. $ n $-dimensional Khalimsky topology).
Sang-Eon Han, Saeid Jafari, Sik Lee
exaly +3 more sources
Extension of continuous functions in digital spaces with the Khalimsky topology
Topology and Its Applications, 2005 The author studies Tietze-type theorems for continuous maps from \({\mathbb Z}^{n}\) to \(\mathbb Z\), where \(\mathbb Z\) has the Khalimsky topology, that is, the topology generated by the subbase \(\{\{2n-1,2n,2n+1\}:n\in{\mathbb Z}\}\) and \({\mathbb Z}^{n}\) has the product Khalimsky topology. The two main results of the article are: 1) For any \(A\
exaly +2 more sources
Theoretical Computer Science, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly +2 more sources
Wireless Communications and Mobile Computing, Volume 2022, Issue 1, 2022., 2022 Wireless body sensor networks (WBSNs) are characterized by a large number of battery‐powered wireless sensor nodes, and the most challenging aspects of WBSNs are sensor node energy consumption, delay, and security (communication and data) while maintaining regular wireless sensor network (WSN) capabilities.
A. Arulprakash +6 more
wiley +1 more source
On Chamfer Distances on the Square and Body‐Centered Cubic Grids: An Operational Research Approach
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 Linear programming is used to solve optimization problems. Thus, finding a shortest path in a grid is a good target to apply linear programming. In this paper, specific bipartite grids, the square and the body‐centered cubic grids are studied. The former is represented as a “diagonal square grid” having points with pairs of either even or pairs of odd ...
Gergely Kovács +5 more
wiley +1 more source
Some Topological Notations via Maki’s Λ‐Sets
Complexity, Volume 2020, Issue 1, 2020., 2020 Our purpose is to present the notions of a β‐Λ‐set and a β‐V‐sets in topological space. We discuss the basic properties of β‐Λ‐sets and β‐V‐sets. Also, the achievement of the topology defined by these families of sets is obtained. Finally, these results are applied to the case of (X, τ) which is the digital n‐space (Zn, Kn) (cf. Section 4).
A. A. Azzam +2 more
wiley +1 more source
The Jordan curve theorem in the Khalimsky plane
Applied General Topology, 2008 The connectivity in Alexandroff topological spaces is equivalent to the path connectivity. This fact gets some specific properties to Z2, equipped with the Khalimsky topology.
Ezzeddine Bouassida
doaj +1 more source