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Topology

Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.

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Map overview Semantic statistics

Topology

Nodes195
Edges194
Triples223
Avg. degree1.99
Density0.010256
Components1

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Topology

Top relations

related to Further reading · 50
Topology → Addison, Art, August Möbius's Marvelous Band, Booksurge, Bourbaki, Breitenberger, Brown, Clifford, Cosmology, December, Dover Publications, Dover Publications Inc, Dr, Elementary Topology, Elements, Gail, Games, Gemignani, General Topology, Graduate Texts
related to history · 23
Topology → Among, Augustin-Louis Cauchy, Bernhard Riemann, Enrico Betti, Euler, Further, German, His, Johann Benedict Listing, Königsberg, Leonhard Euler, Listing, Listing's, Ludwig Schläfli, Nature, November, On, Seven Bridges, Some, The English
related to Bibliography · 21
Topology → Aleksandrov, Birth, Chapter XVIII Topology, Croom, Euler's Gem, Fred, In Aleksandrov, ISBN, Its Content, Kolmogorov, Lavrent'ev, Mathematics, Meaning, Methods, Press, Princeton University Press, Principles, Richeson, Saunders College Publishing, The
related to External links · 21
Topology → America, April, August, Brian McMaster, Elementary Topology, EMS Press, Encyclopedia, First Course Viro, Hassler Whitney, Ivanov, Kharlamov, Mathematics, Netsvetaev, Notes Archived, The Geometry Center, The Topological Zoo, Topology Atlas, Topology Atlas Archived, Topology GlossaryMoscow, Wayback Machine Aisling McCluskey
related to Major books · 21
Topology → Basic, Dover, General, General Topology, ISBN, James, Kelley, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Mineola, Munkres, New Jersey, New York, Prentice Hall, Springer, Springer-Verlag, Stephen, Undergraduate, Upper Saddle River
related to General topology · 10
Topology → Another, Changing, Compact, Connected, General, Intuitively, It, Several, The, This
related to Motivation · 8
Topology → For, In, Kaliningrad, Königsberg, Leonhard Euler, The, This, This Seven Bridges
related to Manifolds · 7
Topology → Euclidean, Examples, Klein, Lines, More, Two-dimensional, While
related to Computer science · 6
Topology → Analyse, Betti, Encode, Replace, The, Topological
related to Differential topology · 6
Topology → Differential, For, It, More, Riemannian, Smooth

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Important terminology

topological spaces set space theory isbn mathematics called algebraic geometric geometry general manifolds continuous one open properties sets basic two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Topologyis aπ-system.The members of τ are called open sets in X0.90text
Topologyis abranch of topology dealing with the basic set-theoretic definitions and constructions used in topology0.90text
Topologyis abranch of mathematics that uses tools from algebra to study topological spaces0.90text
Topologyis afield dealing with differentiable functions on differentiable manifolds0.90text
Topologyis abranch of topology that primarily focuses on low-dimensional manifolds0.90text
slower electrophoresis.Computer scienceTopological data analysis uses techniques from algebraic topology to determine the large-scale structure of a setinstance ofcausing knotting with observable effects0.80text
condensed matter physicsinstance ofproperties.PhysicsTopology is relevant to physics in areas0.80text
quantum field theoryinstance ofproperties.PhysicsTopology is relevant to physics in areas0.80text
quantum computinginstance ofproperties.PhysicsTopology is relevant to physics in areas0.80text
physical cosmology.The topological dependence of mechanical properties in solids is of interest in the disciplines of mechanical engineeringinstance ofproperties.PhysicsTopology is relevant to physics in areas0.80text
materials scienceinstance ofproperties.PhysicsTopology is relevant to physics in areas0.80text
slower electrophoresisinstance ofcausing knotting with observable effects0.80text

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