Relevant bibliographies by topics / Topologı́a Alexandroff

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Academic literature on the topic 'Topologı́a Alexandroff'

Author: Grafiati
Published: 5 June 2025
Last updated: 16 July 2025

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Journal articles on the topic "Topologı́a Alexandroff"

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Pajoohesh, Homeira. "T_0 functional Alexandroff topologies are partial metrizable." Applied General Topology 25, no. 2 (2024): 305–19. http://dx.doi.org/10.4995/agt.2024.19401.

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If f : X → X is a function, the associated functional Alexandroff topology on X is the topology whose closed sets are { A ⊆ X : f ( A ) ⊆ A } . We prove that every functional Alexandroff topology is pseudopartial metrizable and every T0 functional Alexandroff topology is partial metrizable.
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Avila, Jesus, Adriana Grajales, and Leidy Carolina Perdomo-Hernández. "El orden de especialización en estructuras débiles generalizadas." Scientia et technica 24, no. 4 (2019): 628. http://dx.doi.org/10.22517/23447214.20601.

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En topología es bien conocido que podemos pasar de espacios topológicos a conjuntos ordenados y viceversa usando el orden de especialización y la topología de Alexandrov, entre otras. Esta relación ha permitido obtener importantes resultados teóricos, los cuales se han generalizado al considerar relaciones de preorden o mejor aún relaciones binarias. Siguiendo la metodología clásica de los trabajos en matemáticas, es decir usando teoremas, proposiciones, corolarios, ejemplos y contraejemplos, en este trabajo desarrollamos una teoría del orden de especialización en estructuras débiles generaliz
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Dammak, Jamel, and Rahma Salem. "Graphic topology on tournaments." Advances in Pure and Applied Mathematics 9, no. 4 (2018): 279–85. http://dx.doi.org/10.1515/apam-2018-0024.

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Abstract Alexandroff spaces are the topological spaces in which the intersection of arbitrary many open sets is open. Let T be an indecomposable tournament. In this paper, first, we associate a trivial topology to T. Then we define another topology on T, called the graphic topology of T, and we show that it is an Alexandroff topology. Our motivation is to investigate some properties of this topology.
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Zomam, H. O., H. A. Othman, and M. Dammak. "ALEXANDROFF SPACES AND GRAPHIC TOPOLOGY." Advances in Mathematics: Scientific Journal 10, no. 5 (2021): 2653–62. http://dx.doi.org/10.37418/amsj.10.5.28.

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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).
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Viviana, Benavides, та Enrique Vielma Jorge. "T op(X) y Spec(τ ) como espacios primales". Divulgaciones Matemáticas 23-24, № 1-2 (2024): 44–53. https://doi.org/10.5281/zenodo.11539852.

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Una topolog\'ia Alexandroff puede ser definida sobre un conjunto no vac\'io X, a través de una función \(f:X\to X\), decidiendo que los abiertos del espacio son los conjuntos \(A\subset X\) que contienen a su preimagen, es decir \(\tau_f:=\{A\subset X: f^{-1}(A)\subseteq A\}\). Esta topolog\'ia es denominada topología primal, y al espacio \((X, \tau_f)\) se lo llama espacio primal. En este trabajo se explora una topolog\'ia primal \(\tau_\psi\) inducida en \(Top(X)\), a trav\'es de la función \(\psi: Top(X)\to Top(X)\), definida como \(\psi(\tau)=\overline{\tau}\),
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Sudin S. "On some properties of Alexandroff space." International Journal of Science and Research Archive 13, no. 2 (2024): 2563–69. https://doi.org/10.30574/ijsra.2024.13.2.2427.

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The 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 we lose some important spaces such as Euclidean spaces, but the specialized spaces in turn display interesting properties that are not necessary for a standard Euclidean topology.
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Lee, Sik, and Sang-Eon Han. "Semi-separation axioms associated with the Alexandroff compactification of the $ MW $-topological plane." Electronic Research Archive 31, no. 8 (2023): 4592–610. http://dx.doi.org/10.3934/era.2023235.

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<abstract><p>The present paper aims to investigate some semi-separation axioms relating to the Alexandroff one point compactification (Alexandroff compactification, for short) of the digital plane with the Marcus-Wyse ($ MW $-, for brevity) topology. The Alexandroff compactification of the $ MW $-topological plane is called the infinite $ MW $-topological sphere up to homeomorphism. We first prove that under the $ MW $-topology on $ {\mathbb Z}^2 $ the connectedness of $ X(\subset {\mathbb Z}^2) $ with $ X^\sharp\geq 2 $ implies the semi-openness of $ X $. Besides, for the infinite
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Chiaselotti, Giampiero, and Federico G. Infusino. "Alexandroff topologies and monoid actions." Forum Mathematicum 32, no. 3 (2020): 795–826. http://dx.doi.org/10.1515/forum-2019-0283.

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AbstractGiven a monoid S acting (on the left) on a set X, all the subsets of X which are invariant with respect to such an action constitute the family of the closed subsets of an Alexandroff topology on X. Conversely, we prove that any Alexandroff topology may be obtained through a monoid action. Based on such a link between monoid actions and Alexandroff topologies, we firstly establish several topological properties for Alexandroff spaces bearing in mind specific examples of monoid actions. Secondly, given an Alexandroff space X with associated topological closure operator σ, we introduce a
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LAZAAR, SAMI, TOM RICHMOND, and HOUSSEM SABRI. "HOMOGENEOUS FUNCTIONALLY ALEXANDROFF SPACES." Bulletin of the Australian Mathematical Society 97, no. 2 (2017): 331–39. http://dx.doi.org/10.1017/s0004972717000934.

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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.
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Wahyuni, Desy. "TOPOLOGI METRIK PARSIAL." Jurnal Matematika UNAND 1, no. 2 (2012): 71. http://dx.doi.org/10.25077/jmu.1.2.71-78.2012.

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Metrik d di himpunan U adalah suatu fungsi jarak sedemikian sehingga aksiomametrik terpenuhi. Suatu metrik parsial di U merupakan generalisasi minimal dariaksioma metrik sedemikian sehingga setiap objek di U tidak perlu harus mempunyainol jarak dari dirinya sendiri. Topologi metrik parsial adalah topologi yang dibangunoleh basis bola buka metrik parsial, B = fBp"(a)ja 2 U; " > 0g. Topologi metrik parsialdinotasikan dengan T [p]. Salah satu ruang topologi dinotasikan dengan T-ruang. Himpunan(U; ) adalah himpunan urutan parsial atas metrik parsial. Suatu topologi atashimpunan (U; p) disebut t
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Dissertations / Theses on the topic "Topologı́a Alexandroff"

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Menix, Jacob Scott. "Properties of Functionally Alexandroff Topologies and Their Lattice." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3147.

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This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set. The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of function
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Melin, Erik. "Digital Geometry and Khalimsky Spaces." Doctoral thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8419.

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<p>Digital geometry is the geometry of digital images. Compared to Euclid’s geometry, which has been studied for more than two thousand years, this field is very young.</p><p>Efim Khalimsky’s topology on the integers, invented in the 1970s, is a digital counterpart of the Euclidean topology on the real line. The Khalimsky topology became widely known to researchers in digital geometry and computer imagery during the early 1990s.</p><p>Suppose that a continuous function is defined on a subspace of an <i>n-</i>dimensional Khalimsky space. One question to ask is whether this function can be exten
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Book chapters on the topic "Topologı́a Alexandroff"

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Cameron, Douglas E. "The Alexandroff-Sorgenfrey Line." In Handbook of the History of General Topology. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-1756-4_13.

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Gavriluţ, Alina, Ioan Mercheş, and Maricel Agop. "Continuity properties and Alexandroff theorem in Vietoris topology." In Atomicity through Fractal Measure Theory. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29593-6_7.

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Rouyer, Joël, and Costin Vîlcu. "The Connected Components of the Space of Alexandrov Surfaces." In Bridging Algebra, Geometry, and Topology. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09186-0_15.

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Markina, Irina, and Stephan Wojtowytsch. "On the Alexandrov Topology of sub-Lorentzian Manifolds." In Geometric Control Theory and Sub-Riemannian Geometry. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02132-4_17.

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"8. Alexandroff spaces." In General Topology. De Gruyter, 2020. http://dx.doi.org/10.1515/9783110686579-009.

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Bradley, Patrick E., and Norbert Paul. "Topologically Consistent Space, Time, Version, and Scale Using Alexandrov Topologies." In Contemporary Strategies and Approaches in 3-D Information Modeling. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-5625-1.ch003.

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A novel approach to higher dimensional spatial database design is introduced by replacing the canonical solid–face–edge–vertex schema of topological data by a common type SpatialEntity, and the individual “bounded-by” relations between two consecutive classes by one separate binary relation BoundedBy on SpatialEntity defining an Alexandrov topology. This exposes mathematical principles of spatial data design. The first consequence is a mathematical definition of topological “dimension” for spatial data. Another is that every topology for spatial data is an Alexandrov topology. Also, version histories have a canonical Alexandrov topology, and generalizations can be consistently modeled by continuous foreign keys between LoDs. The result is a relational database schema for spatial data of dimension 6 and more, seamlessly integrating space-time, LoDs, and version history. Topological constructions enable queries across these different aspects. Giving points coordinates amounts can give rise to topological inconsistencies which can be measured with topological invariants.
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Herreman, Alain. "H. Seifert and W. Threlfall (1934) and P.S. Alexandroff and H. Hopf (1935), books on Topology." In Landmark Writings in Western Mathematics 1640-1940. Elsevier, 2005. http://dx.doi.org/10.1016/b978-044450871-3/50157-1.

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Journal articles
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