Results 141 to 150 of about 383 (157)
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HOMOGENEOUS FUNCTIONALLY ALEXANDROFF SPACES
Bulletin of the Australian Mathematical Society, 2017A function $f:X\rightarrow X$ determines a topology $P(f)$ on $X$ by taking the closed sets to be those sets $A\subseteq X$ with $f(A)\subseteq A$. The topological space $(X,P(f))$ is called a functionally Alexandroff space. We completely characterise the homogeneous functionally Alexandroff spaces.
SAMI LAZAAR, TOM RICHMOND, HOUSSEM SABRI
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ALEXANDROFF SPACES AND GRAPHIC TOPOLOGY
Advances in Mathematics: Scientific Journal, 2021This work studies and gives some conditions for an Alexandroff space to be graphic topological space by using some basic properties of graphic topology such as locally finitely property. That is, we offer some answer for the open problem which is recalled in \cite{AJK} (Problem 2 page 658).
H.O. Zomam, H.A. Othman, M. Dammak
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ALEXANDROFF SPACES VIA SIMPLICIAL COMPLEXES
JP Journal of Geometry and Topology, 2020Summary: We prove that an Alexandroff space is homotopy equivalent to its shadow space. Previously, simplicial complexes and beat points have been studied on finite spaces. We extend these studies to the infinite case. Along the way, we develop the concepts of beat points and minimal spaces by introducing concepts of super beats and super minimal ...
Mahdi, Hisham, Elostath, Lubna T.
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British Journal of Mathematics & Computer Science, 2015
Each Alexandroff space X has a corresponding shadow space [X] which is T0 Alexandroff space. In this paper, we study Alexandroff spaces and their properties via their shadow spaces. The definitions and the concepts such as Artinian, Noetherian, maximal points and minimal points, that are defined on T0 Alexandroff space carry over to any Alexandroff ...
Hisham Mahdi, S. Nada, Riyad Muamar
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Each Alexandroff space X has a corresponding shadow space [X] which is T0 Alexandroff space. In this paper, we study Alexandroff spaces and their properties via their shadow spaces. The definitions and the concepts such as Artinian, Noetherian, maximal points and minimal points, that are defined on T0 Alexandroff space carry over to any Alexandroff ...
Hisham Mahdi, S. Nada, Riyad Muamar
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Marching Chains algorithm for Alexandroff-Khalimsky spaces
SPIE Proceedings, 2002The Marching Cubes algorithm is a popular method which allows the rendering of 3D binary images, or more generally of iso-surfaces in 3D digital gray-scale images. Yet the original version does not give satisfactory results from a topological point of view, more precisely the extracted mesh is not a coherent surface. This problem has been solved in the
Daragon, Xavier +2 more
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2014
In the following text a proper subclass of Alexandroff topological spaces, namely functional Alexandroff topological spaces, is introduced. We discuss relation between Alexandroff spaces and functional Alexandroff spaces, functional Alexandroff spaces as dynamical systems, and other related topics.
SHİRAZİ, Fatemah Ayatollah Zadeh +1 more
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In the following text a proper subclass of Alexandroff topological spaces, namely functional Alexandroff topological spaces, is introduced. We discuss relation between Alexandroff spaces and functional Alexandroff spaces, functional Alexandroff spaces as dynamical systems, and other related topics.
SHİRAZİ, Fatemah Ayatollah Zadeh +1 more
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A-compactifications and A-weight of Alexandroff spaces
2002Summary: The paper is devoted to the study of the ordered set \(A{\mathcal K}(X,\alpha)\) of all, up to equivalence, \(A\)-compactifications of an Alexandroff space \((X,\alpha)\). The notion of \(A\)-weight (denoted by \(aw(X,\alpha))\) of an Alexandroff space \((X,\alpha)\) is introduced and investigated. Using results from [\textit{A.
CATERINO, Alessandro +2 more
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On some properties of Alexandroff space
International Journal of Science and Research ArchiveThe generalized definition of topology is based on the properties of standard Euclidean topology. The goal of this paper is to study spaces that have topologies, which satisfies the stronger condition namely arbitrary intersection of open sets are open. The topological space with this strong property is known as Alexandroff space. With this restriction
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Structural and Numerical Studies of Some Topological Properties for Alexandroff Spaces
Bulletin of the Iranian Mathematical Society, 2021Sami Lazaar, Houssem Sabri
exaly