Non-Commutative Topology and Quantales

Authors: Coniglio M.E.¹; Miraglia F.²

Source: Studia Logica, Volume 65, Number 2, July 2000 , pp. 223-236(14)

Publisher: Springer

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Abstract:

The relationship between q-spaces (c.f. [9]) and quantum spaces (c.f. [5]) is studied, proving that both models coincide in the case of Spec A, the spectrum of a non-commutative C*-algebra A. It is shown that a sober T_1 quantum space is a classical topological space. This difficulty is circumvented through a new definition of point in a quantale. With this new definition, it is proved that Lid A has enough points. A notion of orthogonality in quantum spaces is introduced, which permits us to express the usual topological properties of separation. The notion of stalks of sheaves over quantales is introduced, and some results in categorial model theory are obtained.

Keywords: non-commutative topology; quantales; Sheaves; C*-algebras

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Philosophy State University of Campinas C.P. 6133, CEP 13081-970 Campinas (SP), Brazil coniglio@cle.unicamp.br 2: Institute for Mathematics and Statistics São Paulo University C.P. 66281, CEP 05315-970 São Paulo (SP), Brazil miraglia@ime.usp.br

Publication date: 2000-07-01