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Zariski topology

In algebraic geometry and commutative algebra, the Zariski topology is a topology defined on geometric objects called varieties. It is very different from topologies that are commonly used in real or complex analysis; in particular, it is not Hausdorff. This topology was introduced primarily by Oscar Zariski and later generalized for making the set of…

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Zariski topology of varieties

Spectrum of a ring

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Map overview Semantic statistics

Zariski topology

Nodes80
Edges79
Triples46
Avg. degree1.98
Density0.025
Components1

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Zariski topology

Top relations

related to Spectrum of a ring · 12
Zariski topology → Again, Hilbert's Nullstellensatz, If, In, Nullstellensatz, Spec, Spm, The, These, Thus, To, Zariski
related to Further properties · 11
Zariski topology → Euclidean, Grothendieck, However, Just, Noetherian, Proj, Spec, The, Then, This, Zariski
related to Properties · 8
Zariski topology → An, As, By Hilbert's, Noetherian, That, The, Zariski, Zariski-closed
related to Examples · 7
Zariski topology → Because, For, If, In, So, Spec, Zariski
related to Zariski topology of varieties · 6
Zariski topology → As, Grothendieck, In, The Zariski, We, Zariski
is a · 2
Zariski topology → topology defined on geometric objects called varieties, weakest topology

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Important terminology

displaystyle closed topology zariski affine ideal set ideals algebraic ring sets spectrum points field maximal prime varieties mathbb spec space

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Zariski topologyis atopology defined on geometric objects called varieties0.90text
Zariski topologyis aweakest topology0.90text
Zariski topologyrelated to ExamplesSpec0.60section
Zariski topologyrelated to ExamplesSo0.60section
Zariski topologyrelated to ExamplesIf0.60section
Zariski topologyrelated to ExamplesZariski0.60section
Zariski topologyrelated to ExamplesBecause0.60section
Zariski topologyrelated to ExamplesIn0.60section
Zariski topologyrelated to ExamplesFor0.60section
Zariski topologyrelated to Further propertiesThe0.60section
Zariski topologyrelated to Further propertiesGrothendieck0.60section
Zariski topologyrelated to Further propertiesHowever0.60section

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    Min side: 3
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    Researching Zariski topology? Use this map to explore Art, Zariski topology of varieties & Spectrum of a ring and other closely related topics, then follow useful entities and relationships into deeper research. Automatically generated connections are research leads, so verify important facts in reliable sources.