Martínez, Juan Carlos On cardinal sequences of scattered spaces. (English) Zbl 0926.54025 Topology Appl. 90, No. 1-3, 187-196 (1998). Summary: It was proved by A. Dow and P. Simon [Algebra Univers. 29, No. 2, 211-226 (1992; Zbl 0786.06011)] that there are \(2^{\omega_1}\) (as many as possible) pairwise nonhomeomorphic compact, \(T_2\), scattered spaces of height \(\omega_1\) and width \(\omega\). In this paper, we prove that if \(\alpha\) is an ordinal with \(\omega_1\leq \alpha< \omega_2\) and \(\theta= \langle \kappa_\xi: \xi<\alpha\rangle\) is a sequence of cardinals such that either \(\kappa_\xi= \omega\) or \(\kappa_\xi= \omega_1\) for every \(\xi< \alpha\), then there are \(2^{\omega_1}\) pairwise nonhomeomorphic compact, \(T_2\), scattered spaces whose cardinal sequence is \(\theta\). Cited in 1 Document MSC: 54G12 Scattered spaces 06E99 Boolean algebras (Boolean rings) Keywords:Cantor-Bendixson derivatives; cardinal sequence Citations:Zbl 0786.06011 PDFBibTeX XMLCite \textit{J. C. Martínez}, Topology Appl. 90, No. 1--3, 187--196 (1998; Zbl 0926.54025) Full Text: DOI References: [1] Baumgartner, J. E.; Shelah, S., Remarks on superatomic Boolean algebras, Ann. Pure Appl. Logic, 33, 109-129 (1987) · Zbl 0643.03038 [2] Dow, A.; Simon, P., Thin-tall Boolean algebras and their automorphism groups, Algebra Universalis, 29, 211-226 (1992) · Zbl 0786.06011 [3] Juhász, I.; Weiss, W., On thin-tall scattered spaces, (Colloq. Math., 40 (1978)), 63-68 · Zbl 0416.54038 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.