Noncommutative topology in mathematics is a term applied to the strictly C*-algebraic part of the noncommutative geometry program. The program has its origins in the Gel'fand duality between the topology of locally compact spaces and the algebraic structure of commutative C*-algebras.
Amongst these are compactness (being unital), dimension (real or stable rank), connectedness (projectionless algebra) and K-theory. So we think of a noncommutative C*-algebra as the algebra of functions on a 'noncommutative space' which does not exist classically.
- Connes, Alain; Consani, Caterina; Marcolli, Matilde (2007), "Noncommutative geometry and motives: the thermodynamics of endomotives", Advances in Mathematics 214 (2): 761–831, arXiv:math.QA/0512138, doi:10.1016/j.aim.2007.03.006, MR 2349719
|This topology-related article is a stub. You can help Wikipedia by expanding it.|