2 00 5 Inverse Limits and Function Algebras ∗ Joan
نویسنده
چکیده
Assuming Jensen’s principle ♦, there is a compact Hausdorff space X which is hereditarily Lindelöf, 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 ♦ 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 βN (Hoffman and Singer).
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