Results 151 to 160 of about 365 (176)

HOMOGENEOUS FUNCTIONALLY ALEXANDROFF SPACES

Bulletin of the Australian Mathematical Society, 2017
A 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, 2021
This 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, 2020
Summary: 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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On Alexandroff Shadow Spaces

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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On metrization of the hit-or-miss topology using Alexandroff compactification

International Journal of Approximate Reasoning, 2007
When the hit-or-miss topology is employed, the space of all closed subsets of a Hausdorff, locally compact and second countable space (HLCSC) is known to be Hausdorff, compact and second countable, thus metrizable. This paper investigates metrics on this
Yangeng Wang
exaly   +2 more sources

Maps generating the same primal space

Quaestiones Mathematicae, 2017
Alexandroff topologies play an enigmatic role in topology. An important family of Alexandroff topologies are the functional Alexandroff spaces introduced by Shirazi and Golestani, and called primal topologies by O. Echi.
Sami Lazaar, Tom Richmond
exaly   +1 more source

Marching Chains algorithm for Alexandroff-Khalimsky spaces

SPIE Proceedings, 2002
The 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, Couprie, Michel, Bertrand, Gilles   +2 more
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Functional Alexandroff Spaces

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, GOLESTANİ, Nasser   +1 more
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The proper homotopy of Alexandroff spaces

Quaestiones Mathematicae
This paper introduces the study of the infinity in the class of Alexandroff spaces by establishing the proper category of locally finite Alexandroff spaces. We observe that the McCord and Clader  heorems are available in this setting. The paper can be considered as the starting point of a seemingly new research: relating the combinatorics and ...
Fern´andez-Bayort, Tom´as, Luque, Alvaro, Quintero, Antonio   +2 more
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A-compactifications and A-weight of Alexandroff spaces

2002
Summary: 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, G. DIMOV, VIPERA, Maria Cristina   +2 more
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