  The compact Hausdorff space X has the Complex Stone-Weierstrass Property
(CSWP) iff it satisfies the complex version of the Stone-Weierstrass Theorem.
W. Rudin showed that all scattered spaces have the CSWP. We describe some
techniques for proving that certain non-scattered spaces have the CSWP. In
particular, if X is the product of a compact ordered space and a compact
scattered space, then X has the CSWP if and only if X does not contain a copy
of the Cantor set.
