The boundedness of the Cantor-Bendixson order of some analytic sets

R. Daniel Mauldin

Vol. 74 (1978), No. 1, 167–177

DOI: 10.2140/pjm.1978.74.167

Abstract

Let X and Y be complete separable metric spaces (Polish spaces). If E is a subset of X × Y , and x ∈ X, then by the x-section of E, E_x, is meant E ∩ ({x}× Y ). By P_s(E) is

In this paper the following uniform boundedness principle for the Cantor-Bendixson order of analytic sets will be demonstrated.

Theorem L. Let W be an analytic subset of X × Y and let M be an analytic subset of X such that M ⊂ P_S(W). Then there is a countable ordinal α such that the α-th Cantor-Bendixson derived set of E_x is empty, for each x in M.

Mathematical Subject Classification 2000

Primary: 54H05

Milestones

Received: 15 March 1976

Published: 1 January 1978