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A theorem on fine connectedness. (English) Zbl 0952.31007

An open connected set in the \(p\)-fine topology, i.e. in the coarsest topology making all \(p\)-superharmonic functions continuous, is called a \(p\)-fine domain. The purpose of this note is to prove the following theorem.
Let \(\Omega\subset{\mathbb R}^n\) be a \(p\)-fine domain for \(1<p\leq n\) and let \(E\subset{\mathbb R}^n\) be a \(p\)-polar. Then \(\Omega\setminus E\) is a \(p\)-fine domain.
As an application of the main result, the author establishes a general version of minimum principle.
Reviewer: K.Malyutin (Sumy)

MSC:

31C15 Potentials and capacities on other spaces
31C45 Other generalizations (nonlinear potential theory, etc.)
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