Noncommutative Cantor–Bendixson derivatives and scattered C⁎-algebras

0488851 - MÚ 2019 RIV NL eng J - Journal Article
Ghasemi, Saeed - Koszmider, P.
Noncommutative Cantor–Bendixson derivatives and scattered C⁎-algebras.
Topology and its Applications. Roč. 240, 15 May (2018), s. 183-209. ISSN 0166-8641. E-ISSN 1879-3207
Institutional support: RVO:67985840
Keywords : C*-algebras * Cantor-Bendixson derivative * scattered locally compact spaces
OECD category: Pure mathematics
Impact factor: 0.416, year: 2018
https://www.sciencedirect.com/science/article/pii/S0166864118301688?via%3Dihub

We analyze the sequence obtained by consecutive applications of the Cantor–Bendixson derivative for a noncommutative scattered C⁎-algebra A, using the ideal IAt(A) generated by the minimal projections of A. With its help, we present some fundamental results concerning scattered C⁎-algebras, in a manner parallel to the commutative case of scattered compact or locally compact Hausdorff spaces and superatomic Boolean algebras. It also allows us to formulate problems which have motivated the “cardinal sequences” programme in the classical topology, in the noncommutative context.
Permanent Link: http://hdl.handle.net/11104/0283373