On basic concepts of non-commutative topology

Non-Commutative Topology and Quantales

Non-Commutative Topology for Curved Quantum Causality

A quantum causal topology is presented. This is modeled after a non-commutative scheme type of theory for the curved finitary spacetime sheaves of the non-abelian incidence Rota algebras that represent ‘gravitational quantum causal sets’. The finitary spacetime primitive algebra scheme structures for quantum causal sets proposed here are interpreted as the kinematics of a curved and reticular l...

Non-commutative Metric Topology on Matrix State Space

We present an operator space version of Rieffel’s theorem on the agreement of the metric topology, on a subset of the Banach space dual of a normed space, from a seminorm with the weak*-topology. As an application we obtain a necessary and sufficient condition for the matrix metric from an unbounded Fredholm module to give the BW-topology on the matrix state space of the C-algebra. Motivated by...

Non Commutative Topology and Local Structure of Operator Algebras

Starting with a W ∗-algebra M we use the inverse system obtained by cutting down M by its (central) projections to define an inverse limit of W ∗-algebras , and show that how this pro-W ∗-algebra encodes the local structure of M . For the C∗-algebras we do the same thing using their atomic enveloping W ∗-algebras . We investigate the relation of these ideas to the Akemann-Giles-Kummer non commu...

Ditopological texture spaces and fuzzy topology, I. Basic concepts

This is the 4rst of three papers which develop various fundamental aspects of the theory of ditopological texture spaces in a categorical setting and present important links with the theory of L-topological spaces. The authors begin by de4ning the notion of q-sets, which together with the p-sets considered earlier, enable the formulation of a powerful concept of duality. This plays an important...