Inverse Limits and Function Algebras

Details Inverse Limits and Function Algebras Inverse Limits and Function Algebras

2005-04-11

arxiv.org/abs/math/0504214v1

Mathematics

General Topology

16 pages

Scientific paper

Assuming Jensen's principle diamond, there is a compact Hausdorff space X which is hereditarily Lindelof, hereditarily separable, and connected, such that no closed subspace of X is both perfect and totally disconnected. The Proper Forcing Axiom implies that there is no such space. The diamond example also fails to satisfy the CSWP (the complex version of the Stone-Weierstrass Theorem). This space cannot contain the two earlier examples of failure of the CSWP, which were totally disconnected -- specifically, the Cantor set (W. Rudin) and beta N (Hoffman and Singer).

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