The Complex Stone-Weierstrass Property
General Topology
2007-05-23 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.math/0305076,
title = {The Complex Stone-Weierstrass Property},
author = {Kenneth Kunen},
journal= {arXiv preprint arXiv:math/0305076},
year = {2007}
}
Comments
15 pages This version extends the main result of the previous version from separable compact ordered spaces to general compact ordered spaces