PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Banach Center Publications

2012 | 98 | 1 | 215-237
Tytuł artykułu

### Finite closed coverings of compact quantum spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space $ℙ^∞$ the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported flabby sheaves of algebras is equivalent to the category of algebras with a finite set of ideals that intersect to zero and generate a distributive lattice. In particular, the Gelfand transform allows us to view finite closed coverings of compact Hausdorff spaces as flabby sheaves of commutative unital C*-algebras over $ℙ^∞$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
215-237
Opis fizyczny
Daty
wydano
2012
Twórcy
autor