Descriptive properties of families of autohomeomorphisms of the unit interval

Let H ⊂ C[0, 1] stand for the Polish space of all increasing autohomeomorphisms of [0, 1].We show that the family of all strictly singular autohomeomorphisms is Π11 -complete. This confirms a suggestion of Graf, Mauldin and Williams. Some related results are also included. © 2008 Elsevier Inc. All rights reserved