OPEN PROBLEMS IN TOPOLOGY

20 Steprans / Steprans’ Problems [ch. 2Question 3.8. If Φ i : P(A i ) ↦→ P(A i ) is an autohomeomorphism for i ∈ ω 35. ?and the sets A i are pairwise disjoint, is there Φ ∈ A such that Φ|P(A i )=Φ ifor each i ∈ ω?ReferencesBlass, A.[1989] Applications of superperfect forcing and its relatives. In Set Theory andits Applications (York 1987), J.Steprāns and W. S. Watson, editors,pages 18–40. Lecture Notes in Mathematics 1401, Springer-Verlag, Berlinetc.Krawczyk, A. and J. Steprans.[19∞] Continuous colourings of topological spaces. unpublished.Rudin, W.[1956] Homogeneity problems in the theory of Čech compactifications. DukeMath. J., 23, 409–419.Shelah, S.[1982] Proper Forcing. Lecture Notes in Mathematics 940, Springer-Verlag,Berlin etc.Shelah, S. and J. Steprans.[1988] PFA implies all automorphisms are trivial. Proc. Amer. Math. Soc.,104(4), 1220–1226.Steprans, J.[1987] The transistivity of autohomeomorphisms of the Čech-Stonecompactification of the integers in the Cohen model. preprint.