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- Title
VIETORIS TOPOLOGY ON HYPERSPACES ASSOCIATED TO A NONCOMMUTATIVE COMPACT SPACE.
- Authors
SADR, MAYSAM MAYSAMI
- Abstract
We study some topological spaces that can be considered as hyper- spaces 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 hyper- space. We also formulate some problems about distances between sub-circles of a quantum torus.
- Subjects
NONCOMMUTATIVE function spaces; ABSTRACT algebra; HAUSDORFF spaces; TOPOLOGICAL spaces; DIFFERENTIAL geometry
- Publication
Mathematica (1222-9016), 2018, Vol 60, Issue 1, p72
- ISSN
1222-9016
- Publication type
Article
- DOI
10.24193/mathcluj.2018.1.08