Hilbert Book Model Project/Relational Structures/fr

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<Hilbert Book Model Project/fr

Structures relationnelles [edit]

Relational structures are sets that restrict the types of their internal relations. Mathematics applies "lattice" as the type name of a category of relational structures.

Lattes[edit]

Un treillis est un ensemble d'éléments qui est fermé pour les connexions et .

Ces connexions obéissent

  • L'ensemble est partiellement ordonné.
    • Cela signifie qu'avec chaque paire d'éléments appartient à un élément , tel que et .
  • L'ensemble est un demi-treillis.
  • Cela signifie qu'avec chaque paire d'éléments un élément existe, tel que.
  • L'ensemble est un demi-treillis..
    • Cela signifie qu'avec chaque paire d'éléments un élément existe, tel que .
  • L'ensemble est un treillis.
    • This means that the set is both a half lattice and a half lattice.

Les relations suivantes se tiennent dans un treillisString Module Error: function rep expects a number as second parameter, received "

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(1)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(2)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(3)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(4)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(5)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(6)

String Module Error: function rep expects a number as second parameter, received "

" Le treillis a une inclusion d'ordre partielle  :String Module Error: function rep expects a number as second parameter, received "

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(7)

String Module Error: function rep expects a number as second parameter, received "

" Un treillis complémentaire contient deux éléments  et et avec chaque élément  un élément complémentaire  tel queString Module Error: function rep expects a number as second parameter, received "

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(8)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(9)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(10)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(11)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(12)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(13)

String Module Error: function rep expects a number as second parameter, received "

" Un treillis ortho-complémentée contient deux éléments  et et avec chaque élément  un élément tel queString Module Error: function rep expects a number as second parameter, received "

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(14)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(15)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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String Module Error: function rep expects a number as second parameter, received "

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est l'élément d'unité; est l'élément nul du treillis

Un treillis distributif soutient les lois distributives:String Module Error: function rep expects a number as second parameter, received "

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String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(19)

String Module Error: function rep expects a number as second parameter, received "

" Un treillis modulaire soutient:String Module Error: function rep expects a number as second parameter, received "

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String Module Error: function rep expects a number as second parameter, received "

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Un treillis modulaire faible supporte à la place:

Il existe un élément  tel queString Module Error: function rep expects a number as second parameter, received "

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(21)

String Module Error: function rep expects a number as second parameter, received "

" obéit:String Module Error: function rep expects a number as second parameter, received "

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String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(23)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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(24)

String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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and

 

 

 

 

(25)

String Module Error: function rep expects a number as second parameter, received "

" Dans un treillis atomiqueString Module Error: function rep expects a number as second parameter, received "

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String Module Error: function rep expects a number as second parameter, received "

"String Module Error: function rep expects a number as second parameter, received "

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or

 

 

 

 

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String Module Error: function rep expects a number as second parameter, received "

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p est un atome.

Treillis bien connus[edit]

La logique classique a la structure d'un treillis ortho-complémentée distributif modulaire et atomique.

La logique quantique a la structure d'un treillis ortho-complémentée faible modulaire et atomique. On l'appelle aussi un treillis orthomodulaire .

Les deux treillisx sont des treillisx atomiques.

Le treillis orthomodulaire trouve une réalisation dans l'ensemble des sous-espaces fermés d'un espace Hilbert séparable. La structure en treillis de cet ensemble est isomorphe au treillis orthomodulaire.

L'ensemble des rays qui sont parcourus par les membres d'une base orthonormée de l'espace de Hilbert forme un ensemble complet d'atomes du treillis orthomodulaire.

Le treillis de configuration modulaire[edit]

L'ensemble des sous-espaces fermés de l'espace de Hilbert est un treillis orthomodulaire, et il contient un sous-ensemble, qui est un sous-treillis et contient les représentants des modules en tant que son éléments,

Les atomes de ce sous-treillis représentent des modules élémentaires. Pour ces raisons, nous appelons le sous-treillis un treillis de configuration modulaire .

Tous les modules possèdent un mécanisme privé qui fournit les emplacements des modules élémentaires que le module contient. Le mécanisme applique un processus stochastique qui possède une fonction caractéristique. Cette fonction caractéristique correspond à la superposition des fonctions caractéristiques des processus qui fournissent les emplacements pour les modules élémentaires individuelles qui constituent le module.

Dans l'espace Hilbert, certains des rays dans le sous-espace de balayage représentent les modules élémentaires. Ces rays sont mutuellement orthogonaux. À chaque instant, un mécanisme privé fournit des modules élémentaires avec un nouvel emplacement.

Dans la vue du créateur, les tubes qui zigzagent avec la valeur de progression contiennent les emplacements d'un module élémentaire correspondant.