Serial compact spaces and the maximal spectrum of a Bézout domain.

Serial quasi-compact T 1 -spaces are exactly the spaces that arise as maximal spectra of Bézout domains. The closed unit interval is serial. A nested sequence of directed graphs is constructed to show that the unit square is still serial. Using arguments of combinatorial set theory, it is proved that big powers of the unit interval are not serial. [ABSTRACT FROM AUTHOR]