The Complex Stone-Weierstrass Property

Details The Complex Stone-Weierstrass Property The Complex Stone-Weierstrass Property

2003-05-05

arxiv.org/abs/math/0305076v2

Mathematics

General Topology

15 pages This version extends the main result of the previous version from separable compact ordered spaces to general compact

Scientific paper

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.

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