Results 21 to 30 of about 75 (63)
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 2, Page 239-249, 1999., 1999 The aim of this paper is to study the class of θ‐generalized closed sets, which is properly placed between the classes of generalized closed and θ‐closed sets. Furthermore, generalized Λ‐sets [16] are extended to θ‐generalized Λ‐sets and R0‐, T1/2‐ and T1‐spaces are characterized.
Julian Dontchev, Haruo Maki
wiley +1 more source
International Journal of Stochastic Analysis, Volume 3, Issue 1, Page 27-55, 1990., 1989 The importance of topological connectedness properties in processing digital pictures is well known. A natural way to begin a theory for this is to give a definition of connectedness for subsets of a digital plane which allows one to prove a Jordan curve theorem.
Efim Khalimsky +2 more
wiley +1 more source
Contractibility and fixed point property: the case of Khalimsky topological spaces [PDF]
Fixed Point Theory and Applications, 2016 AbstractBased on the notions of both contractibility and local contractibility, many works were done in fixed point theory. The present paper concerns a relation between digital contractibility and the existence of fixed points of digitally continuous maps.
openaire +4 more sources
Path-induced closure operators on graphs for defining digital Jordan surfaces
Open Mathematics, 2019 Given a simple graph with the vertex set X, we discuss a closure operator on X induced by a set of paths with identical lengths in the graph. We introduce a certain set of paths of the same length in the 2-adjacency graph on the digital line ℤ and ...
Šlapal Josef
doaj +1 more source
Finite, primitive and euclidean spaces
International Journal of Stochastic Analysis, Volume 1, Issue 3, Page 177-196, 1988., 1988 Integer and digital spaces are playing a significant role in digital image processing, computer graphics, computer tomography, robot vision, and many other fields dealing with finitely or countable many objects. It is proven here that every finite T0‐space is a quotient space of a subspace of some simplex, i.e.
Efim Khalimsky
wiley +1 more source
Galois connections between sets of paths and closure operators in simple graphs
Open Mathematics, 2018 For every positive integer n,we introduce and discuss an isotone Galois connection between the sets of paths of lengths n in a simple graph and the closure operators on the (vertex set of the) graph.
Šlapal Josef
doaj +1 more source
Optimization of WSNs Flooding Rates by Khalimsky Topology
Transactions on Networks and Communications, 2014 In this paper, we proposed a new method of deploying and building an organized architecture of gateway nodes in a Wireless Sensors Network (WSN) formed also by randomly deployed sensors arranged in clusters. This method, based on the Khalimsky theory, reduces the energy consumption and the flooding rates of the conventional flooding algorithm.
Mahmoud Abdellaoui +2 more
openaire +2 more sources
Topological structures in computer science
International Journal of Stochastic Analysis, Volume 1, Issue 1, Page 25-40, 1987., 1987 Topologies of finite spaces and spaces with countably many points are investigated. It is proven, using the theory of ordered topological spaces, that any topology in connected ordered spaces, with finitely many points or in spaces similar to the set of all integers, is an interval‐alternating topology.
Efim Khalimsky
wiley +1 more source
A digital 3D Jordan-Brouwer separation theorem
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaWe introduce a connectedness in the digital space ℤ3 induced by a quaternary relation. Using this connectedness, we prove a digital 3D Jordan-Brouwer separation theorem for boundary surfaces of the digital polyhedra that may be face-to-face tiled with ...
Šlapal Josef
doaj +1 more source
IEEE AccessThis paper poses new challenges, especially when designing routing protocols to improve the quality of service (QoS) criteria and the lifetime of large-scale wireless sensor networks (LS-WSNs) and high sensor node density WSNs (HSND-WSN).
Rahma Gantassi +4 more
doaj +1 more source