This is an announcement for the paper "Inverse limits and function algebras" by Joan E. Hart and Kenneth Kunen.
Abstract: 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).
Archive classification: General Topology; Functional Analysis
Mathematics Subject Classification: 54D05; 46J10
Remarks: 16 pages
The source file(s), invlim.tex: 45668 bytes, is(are) stored in gzipped form as 0504228.gz with size 15kb. The corresponding postcript file has gzipped size 80kb.
Submitted from: kunen@math.wisc.edu
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