A homogeneous extremally disconnected countably compact space (Q1819411)

The authors prove (in ZFC) that there exist infinite homogeneous countably compact extremally disconnected spaces. (This contrasts to the previously known result that infinite homogeneous compact extremally disconnected spaces do not exist). They also produce, using Martin's axiom, two countably compact homogeneous extremally disconnected spaces whose product is not countably compact. Some related open questions are posed.