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Journal articles on the topic 'Topologı́a Alexandroff'

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Published: 5 June 2025

Last updated: 16 July 2025

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1

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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2

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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3

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Mejias, Luis, and Jorge Enrique Vielma. "Avoidance Spectrum of Alexandroff Spaces." Universitas Scientiarum 29, no. 2 (2024): 97–106. http://dx.doi.org/10.11144/javeriana.sc292.taso.

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In this paper we prove that every T0 Alexandroff topological space (X, τ ) is homeomorphic to the avoidance of a subspace of (Spec(Λ), τZ), where Spec(Λ) denotes the prime spectrum of a semi-ring Λ induced by τ and τZ is the Zariski topology. We also prove that (Spec(Λ), τZ) is an Alexandroff space if and only if Λ satisfies the Gilmer property.

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12

Bhattacharjee, Papiya, Michelle L. Knox, and Warren Wm McGovern. "Disconnection in the Alexandroff duplicate." Applied General Topology 22, no. 2 (2021): 331. http://dx.doi.org/10.4995/agt.2021.14602.

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<p>It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space can ever be extremally disconnected. We answer this question in the affirmative; an example of van Douwen is significant. In a slightly different direction we also characterize when the Alexandroff duplicate of a space is a P-space as well as when it is an almost P-space.</p>

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13

Andradi, Hadrian, Chong Shen, Weng Ho, and Dongsheng Zhao. "A new convergence inducing the SI-topology." Filomat 32, no. 17 (2018): 6017–29. http://dx.doi.org/10.2298/fil1817017a.

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In their attempt to develop domain theory in situ T0 spaces, Zhao and Ho introduced a new topology defined by irreducible sets of a resident topological space, called the SI-topology. Notably, the SI-topology of the Alexandroff topology of posets is exactly the Scott topology, and so the SI-topology can be seen as a generalisation of the Scott topology in the context of general T0 spaces. It is well known that the convergence structure that induces the Scott topology is the Scott-convergence - also known as lim-inf convergence by some authors. Till now, it is not known which convergence struct

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14

Arhangel'skii, A. V., and A. N. Dranishnikov. "P.S. Alexandroff and Topology: an introductory note." Topology and its Applications 80, no. 1-2 (1997): 1–6. http://dx.doi.org/10.1016/s0166-8641(96)00180-0.

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15

Szymanski, Andrzej A. "Alexandroff duplicate and βκ". Applied General Topology 23, № 1 (2022): 225–34. http://dx.doi.org/10.4995/agt.2022.15586.

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16

ELFARD, ALI S. R. "SUBMONOIDS OF ABELIAN PARATOPOLOGICAL GROUPS." International Science and Technology Journal 34, no. 2 (2024): 1–11. http://dx.doi.org/10.62341/asrs5329.

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One of the important subclasses of abelian paratopological groups is called the free abelian paratopological group on a topological space. It was introduced in 2003 by Remaguara, Sanchis, and Tkachenko. In this paper, we introduce a single submonoid of the free abelian paratopological group on Alexandroff space, then we prove that this submonoid is a base at the identity element of the free topology of the abelian group. The main result of this paper is to give applications of this submonoid such as studying separation axioms, compactness, and other properties of the free topology on the abeli

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17

Elhamdadi, M., H. Lahrani, and T. Gona. "Topologies, posets and finite quandles." Extracta Mathematicae 38, no. 1 (2023): 1–15. http://dx.doi.org/10.17398/2605-5686.38.1.1.

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An Alexandroff space is a topological space in which every intersection of open sets is open. There is one to one correspondence between Alexandroff T0 -spaces and partially ordered sets (posets). We investigate Alexandroff T0 -topologies on finite quandles. We prove that there is a non-trivial topology on a finite quandle making right multiplications continuous functions if and only if the quandle has more than one orbit. Furthermore, we show that right continuous posets on quandles with n orbits are n-partite. We also find, for the even dihedral quandles, the number of all possible topologie

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18

Alzubaidi, A. M., and M. Dammak. "GRAPHIC TOPOLOGY ON FUZZY GRAPHS." Advances in Mathematics: Scientific Journal 11, no. 10 (2022): 853–68. http://dx.doi.org/10.37418/amsj.11.10.4.

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In this paper, we study the graphic topology $\mathcal{T}_{G}$ for a fuzzy graph. We give some properties of this topology, in particular we prove that $\mathcal{T}_{G}$ is an Alexandroff topology and when two graphs are isomorphic, their graphic topologies will be homeomorphic. We give some properties matching graphs and homeomorphic topology spaces. Finally, we investigate the connectedness of this topology and some relations between the connectedness of the graph and the topology $\mathcal{T}_{G}$.

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19

Szczuka, Paulina. "Properties of the division topology on the set of positive integers." International Journal of Number Theory 12, no. 03 (2016): 775–85. http://dx.doi.org/10.1142/s1793042116500500.

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In this paper, we examine properties of the division topology on the set of positive integers introduced by Rizza in 1993. The division topology on [Formula: see text] with the division order is an example of [Formula: see text]-Alexandroff topology. We mainly concentrate on closures of arithmetic progressions and connected and compact sets. Moreover, we show that in the division topology on [Formula: see text], the continuity is equivalent to the Darboux property.

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20

Stratigos, Panagiotis D. "Some topologies on the set of lattice regular measures." International Journal of Mathematics and Mathematical Sciences 15, no. 4 (1992): 681–95. http://dx.doi.org/10.1155/s0161171292000905.

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We consider the general setting of A.D. Alexandroff, namely, an arbitrary setXand an arbitrary lattice of subsets ofX,ℒ.𝒜(ℒ)denotes the algebra of subsets ofXgenerated byℒandMR(ℒ)the set of all lattice regular, (finitely additive) measures on𝒜(ℒ).First, we investigate various topologies onMR(ℒ)and on various important subsets ofMR(ℒ), compare those topologies, and consider questions of measure repleteness whenever it is appropriate.Then, we consider the weak topology onMR(ℒ), mainly whenℒisδand normal, which is the usual Alexandroff framework. This more general setting enables us to extend var

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21

Gavriluţ, Alina. "Continuity properties and Alexandroff theorem in Vietoris topology." Fuzzy Sets and Systems 194 (May 2012): 76–89. http://dx.doi.org/10.1016/j.fss.2011.12.010.

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22

Zomam, Hanan Omer. "SUPOUT TOPOLOGY ON DIRECTED FUZZY GRAPHS." Advances in Mathematics: Scientific Journal 13, no. 4 (2024): 501–21. http://dx.doi.org/10.37418/amsj.13.4.4.

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In this work, we introduce a topology, called supout topology and denoted $\mathcal{F}^{o}_{\mathcal{G}}$, for a fuzzy directed graph. We study some properties of this topology and give some examples of open and closed sets. We demonstrate that two isomorphic fuzzy directed graphs have homeomorphic supout topologies. In addition, we prove that this topology is an Alexandroff one and then use minimal basis to characterize homeomorphic fuzzy directed graphs. Finally, we investigate the connectedness of this topology vs. the connectivity of the graph.

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23

Mahdi, Hisham, and Lubna T. Elostath. "ALEXANDROFF SPACES VIA SIMPLICIAL COMPLEXES." JP Journal of Geometry and Topology 25, no. 1-2 (2020): 35–55. http://dx.doi.org/10.17654/gt025120035.

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24

McLarty, Colin. "Poor Taste as a Bright Character Trait: Emmy Noether and the Independent Social Democratic Party." Science in Context 18, no. 3 (2005): 429–50. http://dx.doi.org/10.1017/s0269889705000608.

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The creation of algebraic topology required “all the energy and the temperament of Emmy Noether” according to topologists Paul Alexandroff and Heinz Hopf. Alexandroff stressed Noether's radical pro-Russian politics, which her colleagues found in “poor taste”; yet he found “a bright trait of character.” She joined the Independent Social Democrats (USPD) in 1919. They were tiny in Göttingen until that year when their vote soared as they called for a dictatorship of the proletariat. The Minister of the Army and many Göttingen students called them Bolshevist terrorists. Noether's colleague Richard

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25

Valov, V. "Homogeneous ANR-spaces and Alexandroff manifolds." Topology and its Applications 173 (August 2014): 227–33. http://dx.doi.org/10.1016/j.topol.2014.06.001.

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26

Chernov, Vladimir, and Stefan Nemirovski. "Interval topology in contact geometry." Communications in Contemporary Mathematics 22, no. 05 (2019): 1950042. http://dx.doi.org/10.1142/s0219199719500421.

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27

Cogan, Eva. "Lattice Operators and Topologies." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/474356.

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Working within a complete (not necessarily atomic) Boolean algebra, we use a sublattice to define a topology on that algebra. Our operators generalizecomplementon a lattice which in turn abstracts the set theoretic operator. Less restricted than those of Banaschewski and Samuel, the operators exhibit some surprising behaviors. We consider properties of such lattices and their interrelations. Many of these properties are abstractions and generalizations of topological spaces. The approach is similar to that of Bachman and Cohen. It is in the spirit of Alexandroff, Frolík, and Nöbeling, although

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28

Echi, Othman, and Tarek Turki. "Spectral primal spaces." Journal of Algebra and Its Applications 18, no. 02 (2019): 1950030. http://dx.doi.org/10.1142/s0219498819500300.

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Let [Formula: see text] be a mapping. Consider [Formula: see text] Then, according to Echi, [Formula: see text] is an Alexandroff topology. A topological space [Formula: see text] is called a primal space if its topology coincides with an [Formula: see text] for some mapping [Formula: see text]. We denote by [Formula: see text] the set of all fixed points of [Formula: see text], and [Formula: see text] the set of all periodic points of [Formula: see text]. The topology [Formula: see text] induces a preorder [Formula: see text] defined on [Formula: see text] by: [Formula: see text] if and only

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29

Wang, Lan, Xiu-Yun Wu, and Zhen-Yu Xiu. "A degree approach to relationship among fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies." Open Mathematics 17, no. 1 (2019): 913–28. http://dx.doi.org/10.1515/math-2019-0072.

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Abstract In this paper, by means of the implication operator → on a completely distributive lattice M, we define the approximate degrees of M-fuzzifying convex structures, M-fuzzifying closure systems and M-fuzzifying Alexandrov topologies to interpret the approximate degrees to which a mapping is an M-fuzzifying convex structure, an M-fuzzifying closure system and an M-fuzzifying Alexandrov topology from a logical aspect. Moreover, we represent some properties of M-fuzzifying convex structures as well as its relations with M-fuzzifying closure systems and M-fuzzifying Alexandrov topologies by

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30

Gavriluţ, Alina Cristiana. "Alexandroff Theorem in Hausdorff Topology for Null-Null-Additive Set Multifunctions." Annals of the Alexandru Ioan Cuza University - Mathematics 59, no. 2 (2013): 237–51. http://dx.doi.org/10.2478/v10157-012-0046-3.

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Abstract In this paper we further a previous study concerning abstract regularity for monotone set multifunctions, with has immediate applications in well-known situations such as the Borel δ-algebra of a Hausdorff space and/or the Borel (Baire, respectively) δ-ring or δ-ring of a locally compact Hausdorff space. We also study relationships among abstract regularities and other properties of continuity. Especially, a set-valued Alexandroff type theorem is obtained.

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31

Schr�der, Eberhard M. "Ein einfacher Beweis des Satzes von Alexandroff-Lester." Journal of Geometry 37, no. 1-2 (1990): 153–58. http://dx.doi.org/10.1007/bf01230368.

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32

Kim, Yong Chan, and Ju-Mok Oh. "The Relations between Residuated Frames and Residuated Connections." Mathematics 8, no. 2 (2020): 295. http://dx.doi.org/10.3390/math8020295.

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We introduce the notion of (dual) residuated frames as a viewpoint of relational semantics for a fuzzy logic. We investigate the relations between (dual) residuated frames and (dual) residuated connections as a topological viewpoint of fuzzy rough sets in a complete residuated lattice. As a result, we show that the Alexandrov topology induced by fuzzy posets is a fuzzy complete lattice with residuated connections. From this result, we obtain fuzzy rough sets on the Alexandrov topology. Moreover, as a generalization of the Dedekind–MacNeille completion, we introduce R-R (resp. D R - D R ) embed

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33

Wei, Guo, and Yangeng Wang. "On metrization of the hit-or-miss topology using Alexandroff compactification." International Journal of Approximate Reasoning 46, no. 1 (2007): 47–64. http://dx.doi.org/10.1016/j.ijar.2006.12.007.

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34

Han, Sang-Eon. "Properties of space set topological spaces." Filomat 30, no. 9 (2016): 2475–87. http://dx.doi.org/10.2298/fil1609475h.

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Since a locally finite topological structure plays an important role in the fields of pure and applied topology, the paper studies a special kind of locally finite spaces, so called a space set topology (for brevity, SST) and further, proves that an SST is an Alexandroff space satisfying the separation axiom T0. Unlike a point set topology, since each element of an SST is a space, the present paper names the topology by the space set topology. Besides, for a connected topological space (X,T) with |X| = 2 the axioms T0, semi-T1/2 and T1/2 are proved to be equivalent to each other. Furthermore,

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35

Kurt, Nazli, and Kyriakos Papadopoulos. "On Completeness of Sliced Spaces under the Alexandrov Topology." Mathematics 8, no. 1 (2020): 99. http://dx.doi.org/10.3390/math8010099.

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We show that in a sliced spacetime ( V , g ) , global hyperbolicity in V is equivalent to T A -completeness of a slice, if and only if the product topology T P , on V, is equivalent to T A , where T A denotes the usual spacetime Alexandrov “interval” topology.

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Arhangel'skii, A. V. "Locally compact spaces of countable core and Alexandroff compactification." Topology and its Applications 154, no. 3 (2007): 625–34. http://dx.doi.org/10.1016/j.topol.2005.05.011.

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37

Błaszczyk, A., and M. Tkachenko. "Transversal and T1-independent topologies and the Alexandroff duplicate." Topology and its Applications 159, no. 1 (2012): 75–87. http://dx.doi.org/10.1016/j.topol.2011.07.023.

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38

Papadopoulos, Kyriakos, and Nazli Kurt. "On completeness of the Alexandrov topology on a spacetime: Some remarks and questions." International Journal of Geometric Methods in Modern Physics 18, no. 07 (2021): 2150102. http://dx.doi.org/10.1142/s0219887821501024.

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39

Chatyrko, Vitalij, Sang-Eon Han, and Yasunao Hattori. "Some remarks concerning semi-T1/2 spaces." Filomat 28, no. 1 (2014): 21–25. http://dx.doi.org/10.2298/fil1401021c.

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In this paper we prove that each subspace of an Alexandroff T0-space is semi-T1/2. In particular, any subspace of the folder Xn, where n is a positive integer and X is either the Khalimsky line (Z, ?K), the Marcus-Wyse plane (Z2, ?MW) or any partially ordered set with the upper topology is semi-T1/2. Then we study the basic properties of spaces possessing the axiom semi-T1/2 such as finite productiveness and monotonicity.

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40

Paul, Norbert, and Patrick E. Bradley. "Integrating Space, Time, Version, and Scale using Alexandrov Topologies." International Journal of 3-D Information Modeling 4, no. 4 (2015): 64–85. http://dx.doi.org/10.4018/ij3dim.2015100104.

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This article introduces a novel approach to higher dimensional spatial database design. Instead of extending the canonical Solid–Face–Edge–Vertex schema of topological data, these classes are replaced altogether by a common type SpatialEntity, and the individual “bounded-by” relations between two consecutive classes are replaced by one separate binary relation BoundedBy on SpatialEntity which defines a so-called Alexandrov topology on SpatialEntity and thus exposes mathematical principles of spatial data design. This has important consequences: First, a mathematical definition of topological “

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41

Kukieła, Michał Jerzy. "On Homotopy Types of Alexandroff Spaces." Order 27, no. 1 (2009): 9–21. http://dx.doi.org/10.1007/s11083-009-9134-8.

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42

Huang, Jia-Cheng, and Hui-Chun Zhang. "Harmonic Maps Between Alexandrov Spaces." Journal of Geometric Analysis 27, no. 2 (2016): 1355–92. http://dx.doi.org/10.1007/s12220-016-9722-y.

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43

Grove, Karsten, and Peter Petersen. "Alexandrov spaces with maximal radius." Geometry & Topology 26, no. 4 (2022): 1635–68. http://dx.doi.org/10.2140/gt.2022.26.1635.

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44

Foregger, TH, CL Hagopian, and MM Marsh. "The Alexandroff-Urysohn Square and the Fixed Point Property." Fixed Point Theory and Applications 2009, no. 1 (2009): 310832. http://dx.doi.org/10.1155/2009/310832.

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45

McCluskey, A. E., and W. S. Watson. "Minimal TUD spaces." Applied General Topology 3, no. 1 (2002): 55. http://dx.doi.org/10.4995/agt.2002.2112.

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<p>A topological space is T<sub>UD</sub> if the derived set of each point is the union of disjoint closed sets. We show that there is a minimal T<sub>UD</sub> space which is not just the Alexandroff topology on a linear order. Indeed the structure of the underlying partial order of a minimal T<sub>UD</sub> space can be quite complex. This contrasts sharply with the known results on minimality for weak separation axioms.</p>

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46

Forouzesh, F., and S. N. Hosseini. "Reflectional Topology in Residuated Lattices." New Mathematics and Natural Computation 16, no. 03 (2020): 593–608. http://dx.doi.org/10.1142/s1793005720500362.

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In this paper, we introduce soaker filters in a residuated lattice, give some characterizations and investigate some properties of them. Then we define a topology on the set of all the soaker filters, which we call reflectional topology, show it is an Alexandrov topology and give a basis for it. We introduce the notion of join-soaker filters and prove that when the residuated lattice is a join-soaker filter, then the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we prove the reflectional topology is [Formula: see text]

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Rouyer, Joël, and Costin Vîlcu. "Farthest points on most Alexandrov surfaces." Advances in Geometry 20, no. 1 (2020): 139–48. http://dx.doi.org/10.1515/advgeom-2019-0010.

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Mitsuishi, Ayato, and Takao Yamaguchi. "Lipschitz Homotopy Convergence of Alexandrov Spaces." Journal of Geometric Analysis 29, no. 3 (2018): 2217–41. http://dx.doi.org/10.1007/s12220-018-0075-6.

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Hagopian, C. L., and M. M. Marsh. "Generalized Alexandroff–Urysohn squares and a characterization of the fixed point property." Topology and its Applications 157, no. 6 (2010): 997–1001. http://dx.doi.org/10.1016/j.topol.2009.12.015.

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Engel, Alexander, and Martin Weilandt. "Isospectral Alexandrov spaces." Annals of Global Analysis and Geometry 44, no. 4 (2013): 501–15. http://dx.doi.org/10.1007/s10455-013-9378-9.

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