Noncommutative space from dynamical noncommutative geometriesNoncommutative space from dynamical noncommutative geometries
Faculty of Sciences. Mathematics and Computer Science

Fundamental Mathematics

article

2009Bologna, 2009

Mathematics

Journal of geometry and physics. - Bologna

59(2009):2, p. 185-196

0393-0440

000263498600003

E

English (eng)

University of Antwerp

We present noncommutative topology as a basis for noncommutative geometry phrased completely in terms of partially ordered sets with operations. In this note we introduce a noncommutative space-time starting from a dynamical system of noncommutative topologies based on the notion of temporal points. At every moment a commutative topological space is constructed and it is shown to approximate the noncommutative space in sheaf theoretical terms; this so called moment space should be the space where observed phenomena should be described, the commutative shadow of the noncommutative space is to be thought of as the usual space-time.

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