Ordered Spaces, Metric Preimages, and Function Algebras

Details Ordered Spaces, Metric Preimages, and Function Algebras Ordered Spaces, Metric Preimages, and Function Algebras

2005-12-23

arxiv.org/abs/math/0512553v2

Mathematics

General Topology

30 pages. This version uses the author's paper Dissipated Compacta (math.GN/0703429) to simplify and strengthen the results in

Scientific paper

We consider the Complex Stone-Weierstrass Property (CSWP), which is the complex version of the Stone-Weierstrass Theorem. If X is a compact subspace of a product of three linearly ordered spaces, then X has the CSWP if and only if X has no subspace homeomorphic to the Cantor set. In addition, every finite power of the double arrow space has the CSWP. These results are proved using some results about those compact Hausdorff spaces which have scattered-to-one maps onto compact metric spaces.

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