Vietoris topology on hyperspaces associated to a noncommutative compact space Article Swipe

PDF

Related Concepts

Hyperspace Mathematics Hausdorff space Noncommutative geometry Space (punctuation) Topology (electrical circuits) Pure mathematics Hausdorff distance Torus Continuous functions on a compact Hausdorff space Dual space Locally compact space Metric space Normal space Compact space Topological space Discrete mathematics Mathematical analysis Topological vector space Combinatorics Geometry Computer science Operating system

Maysam Maysami Sadr ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.24193/mathcluj.2018.1.08 · OA: W2964156123

We study some topological spaces that can be considered as hyperspaces associated to noncommutative spaces.More precisely, for a NC compact space associated to a unital C * -algebra, we consider the set of closed projections of the second dual of the C * -algebra as the hyperspace of closed subsets of the NC space.We endow this hyperspace with an analog of Vietoris topology.In the case that the NC space has a quantum metric space structure in the sense of Rieffel we study the analogs of Hausdorff and infimum distances on the hyperspace.We also formulate some problems about distances between sub-circles of a quantum torus.