2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67374C(X) denotes the space of continuous complex-valued functions on the compact Hausdorff space X. X has the CSWP if every subalgebra of C(X) which separates points and contains the constant functions is dense in C(X). W. Rudin showed that all scattered X have the CSWP. We describe a class of non-scattered X with the CSWP; by another result of Rudin, such X cannot be metrizable.15 pages This version extends the main result of the previous version from separable compact ordered spaces to general compact ordered spacesGeneral TopologyFunctional Analysis54H13; 46J10text