A Theorem on Fine Connectedness

We prove that E is a p-fine domain whenever R ⁿ is a p-fine domain, E R ⁿ 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.