Search for "Topology" in article titles:

1. Topology: Topology is a branch of advanced mathematics devoted to spatial relationships. It can also be described as the manipulation and mapping of sets. [100%] 2023-02-15 [Mathematics] [Topology]...
2. Topology: Topology is the natural evolution of analysis to a more general level. Whereas analysis was concerned with the implications of continuity on the familiar spaces of R and C, topology seeks to explore all the types of mathematical structures where ... [100%] 2024-01-01 [{{PAGENAME}}] [Introductions]...
3. Topology: When it comes to mathematics, topology (derived from the Greek words "o" meaning "place, location," and "study" meaning "study") is the study of the properties of a geometric object that are preserved under continuous deformations such as stretching, twisting, crumpling ... [100%] 2024-01-01 [Topology] [Mathematical structures]...
4. Topology: In chemistry, topology provides a way of describing and predicting the molecular structure within the constraints of three-dimensional (3-D) space. Given the determinants of chemical bonding and the chemical properties of the atoms, topology provides a model for ... (Chemistry) [100%] 2023-09-20 [Molecular topology] [Molecular geometry]...
5. Topology: Topology (from Greek τόπος - "place" and λόγος - "study") is a branch of mathematics that studies the propeties of objects that are preserved through continuous deformations (such as stretching, bending and compression). "Continuous" means that ruptures (breaking of the object's integrity) and ... [100%] 2023-08-21
6. Topology correction: In computer graphics, topology correction refers to procedures that correct inconsistencies in the topology of a surface mesh that has been obtained from noisy imaging data. [70%] 2024-01-26
7. Topology control: Topology control is a technique used in distributed computing to alter the underlying network (modeled as a graph) to reduce the cost of distributed algorithms if run over the resulting graphs. It is a basic technique in distributed algorithms. (Computing technique) [70%] 2024-01-26 [Network topology] [Wireless sensor network]...
8. Topology optimization: Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system. Topology optimization is different from ... (Mathematical method for optimizing material layout under given conditions) [70%] 2024-01-26 [Mathematical optimization] [Topology]...
9. Topology correction: In computer graphics, topology correction refers to procedures that correct inconsistencies in the topology of a surface mesh that has been obtained from noisy imaging data. [70%] 2023-06-26
10. Topology optimization: Topology optimization (TO) is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system. Topology optimization is different ... (Mathematical method for optimizing material layout under given conditions) [70%] 2023-11-03 [Mathematical optimization] [Topology]...
11. Cosmic Topology: Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi ... [70%] 2021-12-24 [Quantum_Gravity] [Physics]...
12. Topology table: A topology table is used by routers that route traffic in a network. It consists of all routing tables inside the Autonomous System where the router is positioned. [70%] 2023-09-11 [Routing] [Network topology]...
13. Topology control: Topology control is a technique used in distributed computing to alter the underlying network (modeled as a graph) to reduce the cost of distributed algorithms if run over the resulting graphs. It is a basic technique in distributed algorithms. (Computing technique) [70%] 2023-09-11 [Network topology] [Wireless sensor network]...
14. Topology control: Topology control is a technique used in distributed computing to alter the underlying network (modeled as a graph) to reduce the cost of distributed algorithms if run over the resulting graphs. It is a basic technique in distributed algorithms. (Computing technique) [70%] 2023-09-10 [Network topology] [Wireless sensor network]...
15. Topology optimization: Topology optimization (TO) is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system. Topology optimization is different ... (Mathematical method for optimizing material layout under given conditions) [70%] 2023-11-04 [Mathematical optimization] [Topology]...
16. Topology (mathematics): Topology (mathematics) : The study of spatial properties invariant under continuous deformations. (Mathematics) [70%] 2023-06-16
17. Topology optimization: Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system. Topology optimization is different from ... (Mathematical method for optimizing material layout under given conditions) [70%] 2024-03-05 [Mathematical optimization] [Topology]...
18. Journal of Topology: The Journal of Topology is a peer-reviewed scientific journal which publishes papers of high quality and significance in topology, geometry, and adjacent areas of mathematics. It was established in 2008, when the Editorial Board of Topology resigned due to ... [57%] 2024-01-26 [Mathematics journals] [Academic journals established in 2008]...
19. Topology of imbeddings: The branch of topology in which one studies local topological properties of dispositions of closed subsets of a Euclidean space or manifold. The topology of imbeddings arose in the work of A. (Mathematics) [57%] 2024-01-26
20. Counterexamples in Topology: Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. (Book by Lynn Steen) [57%] 2024-01-26 [1978 non-fiction books] [General topology]...
21. Topology of manifolds: The branch of the theory of manifolds (cf. Manifold) concerned with the study of relations between different types of manifolds. (Mathematics) [57%] 2024-01-26
22. Journal of Topology: Journal of Topology est une revue scientifique à comité de lecture de mathématiques dont le sujet est la topologie. Elle a été créée en 2008 à la suite de la démission du comité éditorial de la revue Topology. [57%] 2024-01-26
23. Counterexamples in Topology: Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. (Book by Lynn Steen) [57%] 2023-09-11 [General topology] [Mathematics books]...
24. Journal of Topology: The Journal of Topology is a peer-reviewed scientific journal which publishes papers of high quality and significance in topology, geometry, and adjacent areas of mathematics. It was established in 2008, when the Editorial Board of Topology resigned due to ... [57%] 2023-10-17 [Mathematics journals] [Academic journals established in 2008]...
25. Topology of imbeddings: The branch of topology in which one studies local topological properties of dispositions of closed subsets of a Euclidean space or manifold. The topology of imbeddings arose in the work of A. (Mathematics) [57%] 2023-10-13
26. Counterexamples in Topology: Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. (Book by Lynn Steen) [57%] 2023-09-10 [1978 non-fiction books] [General topology]...
27. Topology of manifolds: The branch of the theory of manifolds (cf. Manifold) concerned with the study of relations between different types of manifolds. (Mathematics) [57%] 2023-10-18
28. Quantum Algebraic Topology: Quantum Algebraic Topology is a theoretical subfield of quantum physics focused on quantum operator algebra and topology of quantum spaces. Both topological quantum field theory and noncommutative geometry may be considered related fields. [57%] 2023-03-03 [Topology]
29. Journal of Topology: Journal of Topology est une revue scientifique à comité de lecture de mathématiques dont le sujet est la topologie. Elle a été créée en 2008 à la suite de la démission du comité éditorial de la revue Topology. [57%] 2023-10-13
30. JTS Topology Suite: JTS Topology Suite (Java Topology Suite) is an open-source Java software library that provides an object model for Euclidean planar linear geometry together with a set of fundamental geometric functions. JTS is primarily intended to be used as a ... (Software) [57%] 2024-09-08 [Geometric algorithms] [Application programming interfaces]...
31. Cocountable topology: In mathematics, the cocountable topology is the topology on a set in which the open sets are those which have countable complement, together with the empty set. Equivalently, the closed sets are the countable sets, together with the whole space. [70%] 2023-07-13
32. Constructible topology: In commutative algebra, the constructible topology on the spectrum \displaystyle{ \operatorname{Spec}(A) }[/math] of a commutative ring \displaystyle{ A }[/math] is a topology where each closed set is the image of \displaystyle{ \operatorname{Spec} (B) }[/math] in \displaystyle{ \operatorname ... [70%] 2023-09-20 [Commutative algebra] [Topology]...
33. DNA topology: DNA topology is the focus of an interdiscipline between molecular biology and mathematics and as a term refers to DNA supercoiling, knotting and catenation. More simply put, DNA topology studies the shape and path of the DNA helix in three ... [70%] 2023-09-29 [Molecular biology] [Molecular topology]...
34. Strong topology: In mathematics, a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on context, and it may refer to: A topology τ is stronger than a topology σ (is ... [70%] 2024-01-04 [Topology]
35. Residual topology: Residual topology is a descriptive stereochemical term to classify a number of intertwined and interlocked molecules, which cannot be disentangled in an experiment without breaking of covalent bonds, while the strict rules of mathematical topology allow such a disentanglement. Examples ... (Physics) [70%] 2023-06-02 [Molecular topology] [Stereochemistry]...
36. Mackey topology: In functional analysis and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves the continuous dual. In other words the Mackey topology does not make linear ... [70%] 2023-09-11 [Topological vector spaces]
37. Algebraic topology: Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. (Branch of mathematics) [70%] 2023-11-05 [Algebraic topology]
38. Cover (topology): In mathematics, and more particularly in set theory, a cover (or covering) of a set \displaystyle{ X }[/math] is a family of subsets of \displaystyle{ X }[/math] whose union is all of \displaystyle{ X }[/math]. More formally, if \displaystyle{ C ... (Topology) [70%] 2024-01-09 [Topology] [General topology]...
39. Lawson topology: In mathematics and theoretical computer science the Lawson topology, named after Jimmie D. Lawson, is a topology on partially ordered sets used in the study of domain theory. [70%] 2023-01-04 [Domain theory] [General topology]...
40. Differential topology: Introduction to Differential Topology by Prof. Justin Sawon Differential topology is a subject in which geometry and analysis are used to obtain topological invariants of spaces, often numerical. [70%] 2023-03-20 [Resources last modified in May 2019] [Topology]...
41. Strong topology (polar topology): In functional analysis and related areas of mathematics the strong topology on the continuous dual space of a topological vector space (TVS) X is the finest polar topology, the topology with the most open sets, on a dual pair. The ... (Polar topology) [70%] 2023-08-22 [Topology of function spaces]
42. Network topology: In the context of a network, topology refers to the way the nodes of the network connect to each other. Networks are classified by the way the links between various nodes are shared. [70%] 2023-02-17 [Networking]
43. Noncommutative topology: In mathematics, noncommutative topology is a term used for the relationship between topological and C*-algebraic concepts. The term has its origins in the Gelfand–Naimark theorem, which implies the duality of the category of locally compact Hausdorff spaces and ... [70%] 2023-07-31 [Banach algebras] [C*-algebras]...
44. Spectrum (topology): In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem. (Topology) [70%] 2023-10-30 [Homotopy theory]
45. Base (topology): In mathematics, a base (or basis; pl.: bases) for the topology τ of a topological space (X, τ) is a family B {\displaystyle {\mathcal {B}}} of open subsets of X such that every open set of the topology is equal to the ... (Topology) [70%] 2023-12-12 [General topology]
46. Interior (topology): In mathematics, the interior of a subset A of a topological space X is the union of all open sets in X that are subsets of A. It is usually denoted by A ∘ {\displaystyle A^{\circ }}. (Topology) [70%] 2023-06-10
47. Upper topology: In mathematics, the upper topology on a partially ordered set X is the coarsest topology in which the closure of a singleton \displaystyle{ \{a\} }[/math] is the order section \displaystyle{ a] = \{x \leq a\} }[/math] for each \displaystyle{ a\in ... [70%] 2022-11-27 [General topology] [Order theory]...
48. Strong topology: A dual pair of vector spaces $ ( L, M) $ over a field $ k $ is a pair of vector spaces $ L $, $ M $ together with a non-degenerate bilinear form over $ k $, $$ \phi : L \times M \rightarrow k. $$ I.e. (Mathematics) [70%] 2023-07-18
49. Euclidean topology: In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on n {\displaystyle n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} by the Euclidean metric. In any metric space, the open balls form a ... (Topological structure of Euclidean space) [70%] 2022-09-09 [Topology]
50. Development (topology): In the mathematical field of topology, a development is a countable collection of open covers of a topological space that satisfies certain separation axioms. Let \displaystyle{ X }[/math] be a topological space. (Topology) [70%] 2023-09-26 [General topology]
51. Lamination (topology): In topology, a branch of mathematics, a lamination is a : A lamination of a surface is a partition of a closed subset of the surface into smooth curves. It may or may not be possible to fill the gaps in ... (Topology) [70%] 2023-09-11 [Topology] [Manifolds]...
52. Flat topology: In mathematics, the flat topology is a Grothendieck topology used in algebraic geometry. It is used to define the theory of flat cohomology; it also plays a fundamental role in the theory of descent (faithfully flat descent). [70%] 2023-09-11 [Algebraic geometry] [Sheaf theory]...
53. Linear topology: In algebra, a linear topology on a left A {\displaystyle A} -module M {\displaystyle M} is a topology on M {\displaystyle M} that is invariant under translations and admits a fundamental system of neighborhood of 0 {\displaystyle 0} that consists ... [70%] 2023-09-13 [Topology] [Topological algebra]...
54. Quantum topology: Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology. Dirac notation provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associated with topological spaces and the ... (Physics) [70%] 2023-09-07 [Quantum mechanics] [Topology]...
55. Differential topology: In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which concerns the geometric properties of smooth ... (Branch of mathematics) [70%] 2023-12-26 [Differential topology]