The Complex Stone-Weierstrass Property
Abstract
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- May 2003
- DOI:
- arXiv:
- arXiv:math/0305076
- Bibcode:
- 2003math......5076K
- Keywords:
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- Mathematics - General Topology;
- Mathematics - Functional Analysis;
- 54H13;
- 46J10
- E-Print:
- 15 pages This version extends the main result of the previous version from separable compact ordered spaces to general compact ordered spaces