The Complex Stone-Weierstrass Property
Abstract
Description
C(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 spaces
15 pages This version extends the main result of the previous version from separable compact ordered spaces to general compact ordered spaces