2003/11/21 by Joan E. Hart, Hart, Joan E., Kenneth Kunen +1 · 1 citation
Mathematics · #46J10 #54C35 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #math.FA #math.GN #msc:46J10 #msc:54C35
paper · pdf · doi:10.48550/arxiv.math/0311392
24 pages
arxiv created 2003/11/21 · arxiv updated 2009/12/01
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.