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Finite closed coverings of compact quantum spaces

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Hajac P., Kaygun A., Zieliński B.

Banach Center Publications

2012

tom 98

nr 1

215-237

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 $ℙ^∞$.

Ograniczanie wyników

1 Banach Center Publications

1 Hajac P.

1 Kaygun A.

1 Zieliński B.

1 2012

Wyniki wyszukiwania

Finite closed coverings of compact quantum spaces