A Theorem on Fine Connectedness |
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Authors: | Latvala Visa |
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Affiliation: | (1) Department of Mathematics, University of Joensuu, P.O. Box 111, 80101 Joensuu, Finland |
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Abstract: | We prove that E is a p-fine domain whenever Rn is a p-fine domain, E Rn is p-polar, and 1 < p n. By a p-fine domain we understand an open connected set in the p-fine topology, i.e. in the coarsest topology making all p-superharmonic functions continuous. As an application of our main result, we establish a general version of minimum principle. |
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Keywords: | Fine topology polar sets minimum principle |
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