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

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content

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

The full text electronic article is available for purchase. You will be able to download the full text electronic article after payment.

$47.00 plus tax      Refund Policy

 

OR

Back to top

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content
Share this item with others: These icons link to social bookmarking sites where readers can share and discover new web pages.
Page Help Click here for Page Help
Shopping cart
Tools
Sign in






Need to register?
Sign up here
Text size: A | A | A | A