On absolute retracts of ω*

An extremally disconnected space is called an absolute retract in the class of all extremally disconnected spaces if it is a retract of any extremally disconnected compact space in which it can be embedded. The Gleason spaces over dyadic spaces have this property. The main result of this paper says that if a space X of π-weight ${\displaystyle {\omega }_1}$ is an absolute retract in the class of all extremally disconnected compact spaces and X is homogeneous with respect to π-weight (i.e. all non-empty open sets have the same π-weight), then X is homeomorphic to the Gleason space over the Cantor cube ${\displaystyle {\{0,1\}}^{{\omega }_1}}$.