Gleason parts separated by smooth curves |
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| Authors: | Bernt Øksendal |
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| Institution: | Department of Mathematics, Agder Distriktshøgskole, Postboks 607, 4601 Kristiansand S., Norway |
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| Abstract: | Suppose Γ is a simple closed C2 curve in the complex plane and let W1, W2 be the components of the complement of Γ. Let X be a compact plane set. Necessary and sufficient conditions are given that any two points x1?X ∩ W1, and x2?X ∩ W2 belong to different Gleason parts for the algebra R(X). We also give an answer to the question: How thin can a nontrivial part for R(X) be ? |
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