Latvala, Visa A theorem on fine connectedness. (English) Zbl 0952.31007 Potential Anal. 12, No. 3, 221-232 (2000). 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) Cited in 7 Documents MSC: 31C15 Potentials and capacities on other spaces 31C45 Other generalizations (nonlinear potential theory, etc.) Keywords:fine topology; \(p\)-fine domain; polar sets; minimum principle PDFBibTeX XMLCite \textit{V. Latvala}, Potential Anal. 12, No. 3, 221--232 (2000; Zbl 0952.31007) Full Text: DOI