Noncommutative Cantor–Bendixson derivatives and scattered C⁎-algebras

0488851 - MÚ 2019 RIV NL eng J - Článek v odborném periodiku
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
Institucionální podpora: RVO:67985840
Klíčová slova: C*-algebras * Cantor-Bendixson derivative * scattered locally compact spaces
Obor OECD: Pure mathematics
Impakt faktor: 0.416, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0283373