For each subset of Baire space, we define, in away similar to a common proof of the Cantor-Bendixson Theorem, a sequence of decreasing subsets S_alpha of N^N, indexed by ordinals. We use this to obtain two new characterizations of the boldface Delta_2^0 Borel pointclass. ADDENDUM: In...
On the Cantor-Bendixson derivative, resolvable ranks, and perfect set theorems of A. H. Stone A Borel derivative on the hyperspace 2X of a compactumX is a Borel monotone mapD: 2X →2X . The derivative determines a Cantor-Bendixson type rank δ:2X →... J Chaber,R Pol - 《Israel Journ...
perfect C-homogeneous sets, then there is a countable ordinal γ such that the Cantor-Bendixson rank of every Chomogeneous set is < γ. In the context of cliques, this strengthens the result of Kojman =-=[2]-=- 1 (see Theorem 3.1(a) below). From our result it follows that if C ...