Complex Function Algebras and Removable Spaces
General Topology
2007-05-23 v1 Functional Analysis
Abstract
The compact Hausdorff space X has the Complex Stone-Weierstrass Property (CSWP) iff it satisfies the complex version of the Stone-Weierstrass Theorem. W. Rudin showed that all scattered spaces have the CSWP. We describe some techniques for proving that certain non-scattered spaces have the CSWP. In particular, if X is the product of a compact ordered space and a compact scattered space, then X has the CSWP if and only if X does not contain a copy of the Cantor set.
Keywords
Cite
@article{arxiv.math/0311392,
title = {Complex Function Algebras and Removable Spaces},
author = {Joan E. Hart and Kenneth Kunen},
journal= {arXiv preprint arXiv:math/0311392},
year = {2007}
}
Comments
24 pages