Π-system

English

Alternative forms

• Template:Alter

Noun

1. Template:Lb A non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.
   • Template:Quote-book
   • Template:Quote-book
   • Template:Quote-text

Usage notes

• By convention, the empty intersection (aka nullary intersection: the "intersection of no sets") is taken to be Ώ itself: its explicit exclusion means that Ώ need not be a member of any arbitrary π-system (i.e., of every π-system).
• The system is said to be a π-system on Ώ.
• For any family Σ of subsets of Ώ, there exists a unique smallest π-system that contains every element of Σ: it is called the π-system generated by Σ.

Hyponyms

• Template:Sense Template:L, Template:L, Template:L

Translations

• French: Template:T, Template:T
• German: Template:T
• Italian: Template:T, Template:T

See also

• Template:L
• Template:L Template:Gloss
• Template:L Template:Gloss
• Template:L

Further reading

• Template:Pedia
• Template:Pedia

Anagrams

• Template:Anagrams