An alternate characterization of the Cantor set

Alan H. Schoenfeld, Gary Gruenhage
1975 Proceedings of the American Mathematical Society  
Let X be a compact metric space such that, up to homeomorphism, X has only two nonempty open subsets.Then X is homeomorphic to the Cantor discontinuum.
doi:10.1090/s0002-9939-1975-0377836-4 fatcat:qbhxsnmqn5gx3jif4dv3pntuzi