On the homogeneity of hyperspaces of dyadic bicompacta (Q1174026)

The main result of this very interesting article states that for every (infinite) dyadic bicompactum \(X\) the hyperspace \(\exp X\) is homogeneous iff \(X\) is homeomorphic to the space of one of the following types: (a) \(X\) a locally connected compactum (metrizable bicompactum) without isolated points (\textit{Curtis, Schori}); (b) \(X=D^{\omega_ 0}\); (c) \(X=D^{\omega_ 1}\) (\textit{Sirota}). The proof is based on some previous results of the author and also on known results of \textit{Shchepin} (\(\tau\)-spectrum), \textit{Choban} and \textit{Solovey-Tannenbaum}. Other results (which are used as steps in the proof) are also significant and in particular enable one to solve problems II.7, II.8 from \textit{Arkhangel'skij's} survey [Russ. Math. Surv. 42, No. 2, 83- 131 (1987); translation from Usp. Mat. Nauk 42, No. 2(254), 69-105 (1987; Zbl 0642.54017)].