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- Mathematical_structure abstract "In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that, in some manner, attach (or relate) to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories.Sometimes, a set is endowed with more than one structure simultaneously; this enables mathematicians to study it more richly. For example, an order induces a topology. As another example, if a set both has a topology and is a group, and the two structures are related in a certain way, the set becomes a topological group.Mappings between sets which preserve structures (so that structures in the domain are mapped to equivalent structures in the codomain) are of special interest in many fields of mathematics. Examples are homomorphisms, which preserve algebraic structures; homeomorphisms, which preserve topological structures; and diffeomorphisms, which preserve differential structures.N. Bourbaki suggested an explication of the concept "mathematical structure" in their book "Theory of Sets" (Chapter 4. Structures) and then defined on that base, in particular, a very general concept of isomorphism.".
- Mathematical_structure wikiPageID "1809181".
- Mathematical_structure wikiPageRevisionID "605338499".
- Mathematical_structure hasPhotoCollection Mathematical_structure.
- Mathematical_structure id "3017".
- Mathematical_structure title "Structure".
- Mathematical_structure subject Category:Mathematical_structures.
- Mathematical_structure subject Category:Set_theory.
- Mathematical_structure subject Category:Type_theory.
- Mathematical_structure type Artifact100021939.
- Mathematical_structure type MathematicalStructures.
- Mathematical_structure type Object100002684.
- Mathematical_structure type PhysicalEntity100001930.
- Mathematical_structure type Structure104341686.
- Mathematical_structure type Whole100003553.
- Mathematical_structure type YagoGeoEntity.
- Mathematical_structure type YagoPermanentlyLocatedEntity.
- Mathematical_structure comment "In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that, in some manner, attach (or relate) to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories.Sometimes, a set is endowed with more than one structure simultaneously; this enables mathematicians to study it more richly. ".
- Mathematical_structure label "Estructura matemática".
- Mathematical_structure label "Mathematical structure".
- Mathematical_structure label "Mathematische Struktur".
- Mathematical_structure label "Structure (mathématiques)".
- Mathematical_structure label "Struktura matematyczna".
- Mathematical_structure label "Struttura (matematica)".
- Mathematical_structure label "Wiskundige structuur".
- Mathematical_structure label "Математическая структура".
- Mathematical_structure label "بنية رياضية".
- Mathematical_structure label "数学的構造".
- Mathematical_structure label "数学结构".
- Mathematical_structure sameAs Matematická_struktura.
- Mathematical_structure sameAs Mathematische_Struktur.
- Mathematical_structure sameAs Estructura_matemática.
- Mathematical_structure sameAs Structure_(mathématiques).
- Mathematical_structure sameAs Struktur_matematika.
- Mathematical_structure sameAs Struttura_(matematica).
- Mathematical_structure sameAs 数学的構造.
- Mathematical_structure sameAs Wiskundige_structuur.
- Mathematical_structure sameAs Struktura_matematyczna.
- Mathematical_structure sameAs m.05ynbb.
- Mathematical_structure sameAs Q748349.
- Mathematical_structure sameAs Q748349.
- Mathematical_structure sameAs Mathematical_structure.
- Mathematical_structure wasDerivedFrom Mathematical_structure?oldid=605338499.
- Mathematical_structure isPrimaryTopicOf Mathematical_structure.