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1

Bartocci, Claudio. "“Ragionare bene su figure disegnate male”: la nascita della Topologia algebrica." Lettera Matematica Pristem 84, no. 1-2 (2013): 22–31. http://dx.doi.org/10.1007/bf03356601.

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2

Peterzil, Ya'acov, and Sergei Starchenko. "Geometry, Calculus and Zil'ber's Conjecture." Bulletin of Symbolic Logic 2, no. 1 (1996): 72–83. http://dx.doi.org/10.2307/421047.

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§1. Introduction. By and large, definitions of a differentiable structure on a set involve two ingredients, topology and algebra. However, in some cases, partial information on one or both of these is sufficient. A very simple example is that of the field ℝ (or any real closed field) where algebra alone determines the ordering and hence the topology of the field:In the case of the field ℂ, the algebraic structure is insufficient to determine the Euclidean topology; another topology, Zariski, is associated with the ield but this will be too coarse to give a diferentiable structure.A celebrated
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3

May, J. P. "Stable Algebraic Topology and Stable Topological Algebra." Bulletin of the London Mathematical Society 30, no. 3 (1998): 225–34. http://dx.doi.org/10.1112/s002460939700427x.

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4

Khan, L. A., N. Mohammad, and A. B. Thaheem. "Double multipliers on topological algebras." International Journal of Mathematics and Mathematical Sciences 22, no. 3 (1999): 629–36. http://dx.doi.org/10.1155/s0161171299226294.

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The main purpose of this paper is to investigate some topological properties of the double multiplier algebra on a topological algebra. LetMd(A)be the double multiplier algebra on a topological algebraA, and letuandsbe the uniform and strong operator topologies onMd(A), respectively. It is shown, under some additional hypotheses onA, that(1)Md(A)isu- ands-complete;(2)Ais au-closed two-sided ideal inMd(A);(3)Aiss-dense inMd(A);(4)sanduhave the same bounded sets;(5) each continuous onto homomorphismϕ:A→Bhas a unique extensionϕ˜:(Md(A),sA)→(Md(B),sB).
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5

Gebbert, Sören, Thomas Leppelt, and Edzer Pebesma. "A Topology Based Spatio-Temporal Map Algebra for Big Data Analysis." Data 4, no. 2 (2019): 86. http://dx.doi.org/10.3390/data4020086.

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Continental and global datasets based on earth observations or computational models challenge the existing map algebra approaches. The available datasets differ in their spatio-temporal extents and their spatio-temporal granularity, which makes it difficult to process them as time series data in map algebra expressions. To address this issue we introduce a new map algebra approach that is topology based. This topology based map algebra uses spatio-temporal topological operators (STTOP and STTCOP) to specify spatio-temporal operations between topological related map layers of different time-ser
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6

Hoffmann, Rudolf-E. "The Injective Hull and the -Compactification of a Continuous Poset." Canadian Journal of Mathematics 37, no. 5 (1985): 810–53. http://dx.doi.org/10.4153/cjm-1985-045-3.

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In [57] (2.12), D. S. Scott showed that the continuous lattices, invented by him in his study of a mathematical theory of computation [56], are precisely (when they are made into topological spaces via the Scott topology) the injective T0-spaces, i.e., the injective objects in the category T0 of T0-spaces and continuous maps with regard to the class of all embeddings. Moreover, the sort of morphisms between continuous lattices Scott considered are precisely the continuous maps with regard to the respective Scott topologies. These are fairly non-Hausdorff topologies. (Indeed, the Scott topology
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7

Gonzaga, Narciso C. "Analyzing Some Structural Properties of Topological B-Algebras." International Journal of Mathematics and Mathematical Sciences 2019 (July 15, 2019): 1–7. http://dx.doi.org/10.1155/2019/8683965.

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In this study, we investigate the topology on B-algebras: an algebraic system of propositional logic. We define here the notion of topological B-algebras (briefly, TB-algebras) and some properties are investigated. A characterization of TB-algebras based on neighborhoods is provided. We also provide a filterbase that generates a unique B-topology, making a TB-algebra in which the filterbase is a neighborhood base of the constant element, provided that the given B-algebra is commutative. Finally, we investigate subalgebras of TB-algebras and introduce the notion of quotient TB-algebras of the g
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8

BHATTACHARJEE, PAPIYA. "TWO SPACES OF MINIMAL PRIMES." Journal of Algebra and Its Applications 11, no. 01 (2012): 1250014. http://dx.doi.org/10.1142/s0219498811005373.

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This paper studies algebraic frames L and the set Min (L) of minimal prime elements of L. We will endow the set Min (L) with two well-known topologies, known as the Hull-kernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min (L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min (L) endowed with the inverse topology is a T1, compact space. The main goal will be to find conditions on L for the spaces Min (L) and Min (L)-1 to have various topological properties; for example, comp
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9

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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10

Bagheri Bardi, G. A., Zbigniew Burdak, and Akram Elyaspour. "The role of the algebraic structure in Wold-type decomposition." Forum Mathematicum 33, no. 4 (2021): 1033–49. http://dx.doi.org/10.1515/forum-2020-0362.

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Abstract In recent works [G. A. Bagheri-Bardi, A. Elyaspour and G. H. Esslamzadeh, Wold-type decompositions in Baer ∗ \ast -rings, Linear Algebra Appl. 539 2018, 117–133] and [G. A. Bagheri-Bardi, A. Elyaspour and G. H. Esslamzadeh, The role of algebraic structure in the invariant subspace theory, Linear Algebra Appl. 583 2019, 102–118], the algebraic analogues of the three major decomposition theorems of Wold, Nagy–Foiaş–Langer and Halmos–Wallen were established in the larger category of Baer * {*} -rings. The results have their versions for commuting pairs in von Neumann algebras. In the cor
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11

Ansari-Toroghy, H., and Sh Habibi. "The quasi-Zariski topology-graph on the maximal spectrum of modules over commutative rings." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 3 (2018): 41–56. http://dx.doi.org/10.2478/auom-2018-0032.

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AbstractLet M be a module over a commutative ring and let Max(M) be the collection of all maximal submodules of M. We topologize Max(M) with quasi-Zariski topology, where M is a Max-top module. For a subset T of Max(M), we introduce a new graph $G(\tau_T^{*m})$, called the quasi-Zariski topology-graph on the maximal spectrum of M. It helps us to study algebraic (resp. topological) properties of M (resp. Max(M)) by using the graphs theoretical tools.
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12

Raussen, Martin. "Strictifying and taming directed paths in Higher Dimensional Automata." Mathematical Structures in Computer Science 31, no. 2 (2021): 193–213. http://dx.doi.org/10.1017/s0960129521000128.

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AbstractDirected paths have been used by several authors to describe concurrent executions of a program. Spaces of directed paths in an appropriate state space contain executions with all possible legal schedulings. It is interesting to investigate whether one obtains different topological properties of such a space of executions if one restricts attention to schedulings with “nice” properties, e.g. involving synchronisations. This note shows that this is not the case, i.e. that one may operate with nice schedulings without inflicting any harm. Several of the results in this note had previousl
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13

Caprau, Carmen. "Twin TQFTs and Frobenius Algebras." Journal of Mathematics 2013 (2013): 1–25. http://dx.doi.org/10.1155/2013/407068.

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We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on atwin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra(C,W,z,z∗)consists of a commutative Frobenius algebraC, a symmetric Frobenius algebraW, and an algebra homomorphismz:C→Wwith dualz∗:W→C, satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show
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14

Rodabaugh, S. E. "Relationship of Algebraic Theories to Powerset Theories and Fuzzy Topological Theories for Lattice-Valued Mathematics." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–71. http://dx.doi.org/10.1155/2007/43645.

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This paper deals with a broad question—to what extent is topology algebraic—using two specific questions: (1) what are the algebraic conditions on the underlying membership lattices which insure that categories for topology and fuzzy topology are indeed topological categories; and (2) what are the algebraic conditions which insure that algebraic theories in the sense of Manes are a foundation for the powerset theories generating topological categories for topology and fuzzy topology? This paper answers the first question by generalizing the Höhle-Šostak foundations for fixed-basis lattice-valu
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15

Akbarbaglu, I., and S. Maghsoudi. "On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups." Abstract and Applied Analysis 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/947908.

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Let be a locally compact group with a fixed left Haar measure and be a system of weights on . In this paper, we deal with locally convex space equipped with the locally convex topology generated by the family of norms . We study various algebraic and topological properties of the locally convex space . In particular, we characterize its dual space and show that it is a semireflexive space. Finally, we give some conditions under which with the convolution multiplication is a topological algebra and then characterize its closed ideals and its spectrum.
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16

., Sulastri. "OPERATOR BATAS PADA HOMOLOGI KUBIK." Jurnal Matematika UNAND 2, no. 4 (2013): 73. http://dx.doi.org/10.25077/jmu.2.4.73-82.2013.

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Algebra topology is a concept that classifies topological spaces particularlycubical sets based on the context of the algebraic objects namely homology groups. Atopological problem can also be viewed from the point of view of combinatorics whichcan be simplified to be graphs. In this paper it is discussed about the classification ofthe cubical sets based on its homology groups using the concept of boundary operatorsas homomorphisms of free Abelian groups.
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17

Arhippainen, Jorma. "On functional representation of locallym-pseudoconvex algebras." International Journal of Mathematics and Mathematical Sciences 22, no. 2 (1999): 223–37. http://dx.doi.org/10.1155/s0161171299222235.

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Functional representation of a topological algebra(A,T)has been studied in many papers under various assumptions for the topologyTonA. Usually the imageAˆof the Gelfand map has been equipped with the compact-open topology. This leads, in several cases, to such kind of difficulties as, for instance, that the Gelfand map is not necessarily continuous or that the compact-open topology is not of the same type as the topologyT. In this paper, we study locallym-pseudoconvex algebras and provideAˆwith such kind of topology that the above two claims are fulfilled. By using this representation the desc
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18

Liu, Bo, Housheng Su, Licheng Wu, and Shengchao He. "A New Perspective to Algebraic Characterization on Controllability of Multiagent Systems." Complexity 2020 (March 27, 2020): 1–12. http://dx.doi.org/10.1155/2020/9703972.

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Recently, algebraic characterization of multiagent controllability through its topology has been widely concerned by the systems and control community. The controllability of leader-follower networked multiagent systems under the framework of generic linear dynamics is firstly discussed via λ-matrix. Some new algebra-theoretic necessary and/or sufficient conditions of the controllability for generic linear multiagent systems are established. Moreover, the controllable conditions for multiagent networks with special topological graphs through λ-matrix are presented.
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19

Miller, John Boris. "The natural ordering on a strictly real Banach algebra." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 3 (1990): 539–56. http://dx.doi.org/10.1017/s0305004100068808.

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AbstractA strictly real unital Banach algebra is one in which every element has real spectrum. An antilattice partial order and its associated open-interval topology are defined on by taking as positive cone the principal component of the maximal group of the algebra, and their properties are studied. The topology coincides with the semimetric topology of the spectral radius, which is a seminorm, making into a locally convex partially ordered topological algebra with continuous inversion and normal cone. Every positive element has a unique positive square root, and logarithm, and these functio
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20

Mancao, Jemil, and Sergio Canoy. "Another Look at Topological BCH-algebras." European Journal of Pure and Applied Mathematics 13, no. 4 (2020): 730–38. http://dx.doi.org/10.29020/nybg.ejpam.v13i4.3842.

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A BCH-algebra (H, ⁕ ,0) furnished with a topology τ on H (also called a BCH-topology on H) is called a topological BCH-algebra (or TBCH-algebra) if the function ⁕: H ×H → H, defined by ⁕((x, y)) =x ⁕ y for any x,y in H, is continuous, where the Cartesian product topology on H × H is furnished by τ. In this paper, we give other structural properties of topological BCH-algebras.
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Belleza, Katrina Eusebio, and Jocelyn Vilela. "On B-ideals in a Topological B-Algebra." European Journal of Pure and Applied Mathematics 13, no. 4 (2020): 830–39. http://dx.doi.org/10.29020/nybg.ejpam.v13i4.3807.

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This paper presents the characterizations and properties of B-ideals in a topological B-algebra and introduces the uniform topology on a B-algebra in terms of its B- ideals. Moreover, this paper shows that a uniform B-topological space is a topological B-algebra.
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22

Kurilic, Milos, and Aleksandar Pavlovic. "The left, the right and the sequential topology on Boolean algebras." Filomat 33, no. 14 (2019): 4451–59. http://dx.doi.org/10.2298/fil1914451k.

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For the algebraic convergence ?s, which generates the well known sequential topology ?s on a complete Boolean algebra B, we have ?s = ?ls ? ?li, where the convergences ?ls and ?li are defined by ?ls(x) = {lim sup x}? and ?li(x) = {lim inf x+}? (generalizing the convergence of sequences on the Alexandrov cube and its dual). We consider the minimal topology Olsi extending the (unique) sequential topologies O?s (left) and O?li (right) generated by the convergences ?ls and ?li and establish a general hierarchy between all these topologies and the corresponding a priori and a posteriori convergence
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Alqahtani, Mesfer Hayyan, Cenap Özel, and Ibtesam Alshammari. "New Topology on Omega Algebra." European Journal of Pure and Applied Mathematics 13, no. 3 (2020): 513–28. http://dx.doi.org/10.29020/nybg.ejpam.v13i3.3764.

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The purpose of this paper is to define a new topology called omega topology over a new structure called omega algebra and discuss some of its topological properties. Four different examples of omega topology are introduced. Furthermore, we define a new topology over a semiring in conventional algebra and we study the relationship between omega topology and weaker kinds of normality.
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Azhari, Mohammed El. "Multipliers of Uniform Topological Algebras." Annales Mathematicae Silesianae 31, no. 1 (2017): 71–81. http://dx.doi.org/10.1515/amsil-2017-0002.

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Abstract Let E be a complete uniform topological algebra with Arens-Michael normed factors within an algebra isomorphism ϕ. If each factor Eα is complete, then every multiplier of E is continuous and ϕ is a topological algebra isomorphism where M(E) is endowed with its seminorm topology.
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Stoltenberg-Hansen, V., and J. V. Tucker. "Complete local rings as domains." Journal of Symbolic Logic 53, no. 2 (1988): 603–24. http://dx.doi.org/10.1017/s0022481200028498.

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Contents: Introduction. §1: Computable rings and modules. §2: Ideal membership relation. §3: Effective structured domains. §4: Completion of a local ring as a domain. §5: The recursive completion. Epilogue. References.Introduction. Completion is an important general mathematical device. Often, but not always, a completion takes the following form. Let A be a topological algebraic structure whose topology is derived from a metric. For A, a topological algebra  and an embedding i: A →  are constructed such that  is a complete metric space in which A is densely embedded by i. The long list of
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Abuhlail, Jawad, and Hamza Hroub. "Zariski-like topologies for lattices with applications to modules over associative rings." Journal of Algebra and Its Applications 18, no. 07 (2019): 1950131. http://dx.doi.org/10.1142/s0219498819501317.

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We study Zariski-like topologies on a proper class [Formula: see text] of a complete lattice [Formula: see text]. We consider [Formula: see text] with the so-called classical Zariski topology [Formula: see text] and study its topological properties (e.g. the separation axioms, the connectedness, the compactness) and provide sufficient conditions for it to be spectral. We say that [Formula: see text] is [Formula: see text]-top if [Formula: see text] is a topology. We study the interplay between the algebraic properties of an [Formula: see text]-top complete lattice [Formula: see text] and the t
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ANTOINE, J. P., F. BAGARELLO, and C. TRAPANI. "TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES." Reviews in Mathematical Physics 11, no. 03 (1999): 267–302. http://dx.doi.org/10.1142/s0129055x99000106.

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Let [Formula: see text] be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space [Formula: see text]. Then [Formula: see text] is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of [Formula: see text]. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of Lp spaces on [0, 1] or on ℝ, amalgam spaces), o
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Petrovic, Zoran. "Boolean algebras in algebraic topology." Publications de l'Institut Math?matique (Belgrade), no. 96 (2007): 135–39. http://dx.doi.org/10.2298/pim0796135p.

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29

NURAKUNOV, ANVAR M., and MICHAŁ M. STRONKOWSKI. "PROFINITENESS IN FINITELY GENERATED VARIETIES IS UNDECIDABLE." Journal of Symbolic Logic 83, no. 04 (2018): 1566–78. http://dx.doi.org/10.1017/jsl.2017.89.

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AbstractProfinite algebras are exactly those that are isomorphic to inverse limits of finite algebras. Such algebras are naturally equipped with Boolean topologies. A variety ${\cal V}$ is standard if every Boolean topological algebra with the algebraic reduct in ${\cal V}$ is profinite.We show that there is no algorithm which takes as input a finite algebra A of a finite type and decide whether the variety $V\left( {\bf{A}} \right)$ generated by A is standard. We also show the undecidability of some related properties. In particular, we solve a problem posed by Clark, Davey, Freese, and Jacks
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30

KAZAMA, YOICHI. "NOVEL TOPOLOGICAL CONFORMAL ALGEBRAS." Modern Physics Letters A 06, no. 14 (1991): 1321–32. http://dx.doi.org/10.1142/s0217732391001421.

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Algebraic characterization of 2-dimensional topological conformal field theories (TCFT’s) is proposed and some of its consequences are studied. In particular, we find two kinds of novel closed algebras, both of which are non-trivial extensions of the twisted version of the N=2 superconformal algebra. The larger of these algebras generically allows non-vanishing central charge c, a simple example of which is provided by a system with c=−2. The other algebra, on the other hand, requires vanishing central charge. An intriguing feature of this algebra is that it can be “untwisted” to yield a sligh
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31

Kirişci, Murat. "Integrated and Differentiated Spaces of Triangular Fuzzy Numbers." Fasciculi Mathematici 59, no. 1 (2017): 75–89. http://dx.doi.org/10.1515/fascmath-2017-0018.

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AbstractFuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Fuzzy sets have be- come popular in every branch of mathematics such as analysis, topology, algebra, applied mathematics etc. Thus fuzzy sets triggered the creation of a wide range of research topics in all areas of science in a short time. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate t
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32

Arnold, Douglas N., Richard S. Falk, and Ragnar Winther. "Finite element exterior calculus, homological techniques, and applications." Acta Numerica 15 (May 2006): 1–155. http://dx.doi.org/10.1017/s0962492906210018.

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Finite element exterior calculus is an approach to the design and understanding of finite element discretizations for a wide variety of systems of partial differential equations. This approach brings to bear tools from differential geometry, algebraic topology, and homological algebra to develop discretizations which are compatible with the geometric, topological, and algebraic structures which underlie well-posedness of the PDE problem being solved. In the finite element exterior calculus, many finite element spaces are revealed as spaces of piecewise polynomial differential forms. These conn
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33

Hilton, Peter. "A new look at means on topological spaces." International Journal of Mathematics and Mathematical Sciences 20, no. 4 (1997): 617–20. http://dx.doi.org/10.1155/s0161171297000859.

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34

Long, Botao, and Wei Wu. "Isometry groups of twisted reduced group C∗-algebras." International Journal of Mathematics 28, no. 14 (2017): 1750101. http://dx.doi.org/10.1142/s0129167x17501014.

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An isometry of a unital [Formula: see text]-algebra with respect to a spectral triple is a [Formula: see text]-automorphism of the [Formula: see text]-algebra given by the conjugation by a unitary operator which commutes with the Dirac operator. We give a semidirect product topological characterization on the isometry group of a twisted reduced group [Formula: see text]-algebra of a discrete group with respect to the standard spectral triple induced by a length function on the group. We prove that this isometry group is compact in the point-norm topology, and in particular, for a finitely gene
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Rostami, Esmaeil, Masoumeh Hedayati, and Nosratollah Shajareh Poursalavati. "The flat topology on the minimal and maximal prime spectrum of a commutative ring." Journal of Algebra and Its Applications 18, no. 06 (2019): 1950110. http://dx.doi.org/10.1142/s021949881950110x.

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In this paper, we investigate connections between some algebraic properties of commutative rings and topological properties of their minimal and maximal prime spectrum with respect to the flat topology. We show that for a commutative ring [Formula: see text], the ascending chain condition on principal annihilator ideals of [Formula: see text] holds if and only if [Formula: see text] is a Noetherian topological space as a subspace of [Formula: see text] with respect to the flat topology and we give a characterization for a topological space [Formula: see text] for which [Formula: see text] is a
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36

Bose, Bedanta, and Angsuman Das. "Graph theoretic representation of rings of continuous functions." Filomat 34, no. 10 (2020): 3417–28. http://dx.doi.org/10.2298/fil2010417b.

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In this paper, we introduce a graph structure, called zero-set intersection graph ?(C(X)), on the ring of real valued continuous functions, C(X), on a Tychonoff space X. We show that the graph is connected and triangulated. We also study the inter-relationship of cliques of ?(C(X)) and ideals in C(X) which helps to characterize the structure of maximal cliques of ?(C(X)) by different kind of maximal ideals of C(X). We show that there are at least 2c many different maximal cliques which are never graph isomorphic to each other. Furthermore, we study the neighbourhood properties of a vertex and
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RIEČANOVÁ, ZDENKA. "STATES, UNIFORMITIES AND METRICS ON LATTICE EFFECT ALGEBRAS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, supp01 (2002): 125–33. http://dx.doi.org/10.1142/s0218488502001879.

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We show that every state ω on a lattice effect algebra E induces a uniform topology on E. If ω is subadditive this topology coincides with pseudometric topology induced by ω. Further, we show relations between the interval and order topology on E and topologies induced by states.
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Glinos, Nikolaos, and George Nakos. "An application of computer algebra to algebraic topology." International Journal of Computer Mathematics 34, no. 1-2 (1990): 33–41. http://dx.doi.org/10.1080/00207169008803861.

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39

Ballico, E. "On vector bundles on algebraic surfaces and 0-cycles." Nagoya Mathematical Journal 130 (June 1993): 19–23. http://dx.doi.org/10.1017/s0027763000004402.

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Let X be an algebraic complex projective surface equipped with the euclidean topology and E a rank 2 topological vector bundle on X. It is a classical theorem of Wu ([Wu]) that E is uniquely determined by its topological Chern classes . Viceversa, again a classical theorem of Wu ([Wu]) states that every pair (a, b) ∈ (H (X, Z), Z) arises as topological Chern classes of a rank 2 topological vector bundle. For these results the existence of an algebraic structure on X was not important; for instance it would have been sufficient to have on X a holomorphic structure. In [Sch] it was proved that f
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LINDNER, SEBASTIAN. "RESOLVABILITY PROPERTIES OF SIMILAR TOPOLOGIES." Bulletin of the Australian Mathematical Society 92, no. 3 (2015): 470–77. http://dx.doi.org/10.1017/s0004972715001021.

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We demonstrate that many properties of topological spaces connected with the notion of resolvability are preserved by the relation of similarity between topologies. Moreover, many of them can be characterised by the properties of the algebra of sets with nowhere dense boundary and the ideal of nowhere dense sets. We use these results to investigate whether a given pair of an algebra and an ideal is topological.
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Pal, Priyanka, S. P. Tiwari, and Renu Verma. "Different Operators in Automata Theory Based on Residuated and Co-Residuated Lattices." New Mathematics and Natural Computation 15, no. 01 (2018): 169–90. http://dx.doi.org/10.1142/s1793005719500108.

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This paper is towards the algebraic and topological study of automata based on residuated and co-residuated lattices via different operators. The interrelationships among the operators are discussed. Interestingly, we show that the algebraic concepts of an automaton based on a residuated and co-residuated lattice can be expressed in terms of [Formula: see text]-topology/co-topology induced by operators. Finally, a composition of such automata is introduced and its categorical significance is discussed.
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42

Khalaf, Alias. "On S-topological Bck-algebra." Journal of Duhok University 23, no. 1 (2020): 199–208. http://dx.doi.org/10.26682/csjuod.2020.23.1.21.

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The aim of this paper is to introduce the concept of s- topological BCK-algebras which is a BCK-algebra equipped with a spe- cial type of topology that makes the operation defined on it s-topologically continuous
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43

Nahlus, Nazih. "Lie Algebras of Pro-Affine Algebraic Groups." Canadian Journal of Mathematics 54, no. 3 (2002): 595–607. http://dx.doi.org/10.4153/cjm-2002-021-9.

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AbstractWe extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed fieldKof characteristic 0. However, some modifications are needed in some extensions. So we introduce the pro-discrete topology on the Lie algebra ℒ(G) of the pro-affine algebraic groupGoverK, which is discrete in the finite-dimensional case and linearly compact in general. As an example, ifLis any sub Lie algebra of ℒ(G), we show that the closure of [L,L] in ℒ(G) is algebraic in ℒ(G).We also discuss the Hopf algebra of representative functions H
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Ferretti, Elena. "On the Relationship between Primal/Dual Cell Complexes of the Cell Method and Primal/Dual Vector Spaces: an Application to the Cantilever Elastic Beam with Elastic Inclusion." Curved and Layered Structures 6, no. 1 (2019): 77–89. http://dx.doi.org/10.1515/cls-2019-0007.

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AbstractThe Cell Method (CM) is an algebraic numerical method based on the use of global variables: the configuration, source and energetic global variables. The configuration variables with their topological equations, on the one hand, and the source variables with their topological equations, on the other hand, define two vector spaces that are a bialgebra and its dual algebra. The operators of these topological equations are generated by the outer product of the geometric algebra, for the primal vector space, and by the dual product of the dual algebra, for the dual vector space. The topolo
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Burgin, M. S. "Topology in nonlinear extensions of hypernumbers." Discrete Dynamics in Nature and Society 2005, no. 2 (2005): 145–70. http://dx.doi.org/10.1155/ddns.2005.145.

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Modern theory of dynamical systems is mostly based on nonlinear differential equations and operations. At the same time, the theory of hypernumbers and extrafunctions, a novel approach in functional analysis, has been limited to linear systems. In this paper, nonlinear structures are introduced in spaces of real and complex hypernumbers by extending the concept of a hypernumber. In such a way, linear algebras of extended hypernumbers are built. A special topology of conical neighborhoods in these algebras is introduced and studied. It is proved that the space of all extended real hypernumbers
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Ceniceros, Jose, Mohamed Elhamdadi, and Alireza Mashaghi. "Coloring Invariant for Topological Circuits in Folded Linear Chains." Symmetry 13, no. 6 (2021): 919. http://dx.doi.org/10.3390/sym13060919.

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Circuit topology is a mathematical approach that categorizes the arrangement of contacts within a folded linear chain, such as a protein molecule or the genome. Theses linear biomolecular chains often fold into complex 3D architectures with critical entanglements and local or global structural symmetries stabilised by formation of intrachain contacts. Here, we adapt and apply the algebraic structure of quandles to classify and distinguish chain topologies within the framework of circuit topology. We systematically study the basic circuit topology motifs and define quandle/bondle coloring for t
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Forouzesh, F., E. Eslami, and A. Borumand Saeid. "Spectral Topology on MV-Modules." New Mathematics and Natural Computation 11, no. 01 (2015): 13–33. http://dx.doi.org/10.1142/s1793005715500027.

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In this paper, the spectral topology and quasi-spectral topology of proper prime A-ideals in an MV-module are introduced. We show that the spectral topology of proper ⋅-prime ideals of a PMV-algebra with unity for product, is the same as the spectral topology of proper prime ideals in an MV-algebra. Also we show that the set of all prime A-ideals in an MV-module with spectral topology is not T0 and T1 topological spaces but quasi-spectral topology is T0-space and is not T1-space. Finally, we investigate when the set of all prime A-ideals in an MV-module are Hausdorff and disconnected.
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Bagchi, Susmit. "Analysis of Topological Endomorphism of Fuzzy Measure in Hausdorff Distributed Monoid Spaces." Symmetry 11, no. 5 (2019): 671. http://dx.doi.org/10.3390/sym11050671.

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The concepts of fuzzy sets and topology are widely applied to model various algebraic structures and computations. The dynamics of fuzzy measures in topological spaces having distributed monoid embeddings is an interesting topic in the presence of topological endomorphism. This paper presents the analysis of topological endomorphism and the properties of topological fuzzy measures in distributed monoid spaces. The topological space is considered to be Hausdorff and second countable in nature. The analysis of consistency of fuzzy measure in endomorphic topological spaces is formulated. The alge
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Denniston, Jeffrey T., Austin Melton, and Stephen E. Rodabaugh. "Interweaving algebra and topology: Lattice-valued topological systems." Fuzzy Sets and Systems 192 (April 2012): 58–103. http://dx.doi.org/10.1016/j.fss.2011.07.001.

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Çeken, Seçil. "On the upper dual Zariski topology." Filomat 34, no. 2 (2020): 483–89. http://dx.doi.org/10.2298/fil2002483c.

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Let R be a ring with identity and M be a left R-module. The set of all second submodules of M is called the second spectrum of M and denoted by Specs(M). For each prime ideal p of R we define Specsp(M) := {S? Specs(M) : annR(S) = p}. A second submodule Q of M is called an upper second submodule if there exists a prime ideal p of R such that Specs p(M)? 0 and Q = ? S2Specsp(M)S. The set of all upper second submodules of M is called upper second spectrum of M and denoted by u.Specs(M). In this paper, we discuss the relationships between various algebraic properties of M and the topological condi
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