Quasiopen and p-path open sets, and characterizations of quasicontinuity

Abstract

In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincaré inequality we show that quasiopen and p-path open sets coincide. Under the same assumptions we show that all Newton-Sobolev functions on quasiopen sets are quasicontinuous.

17 pages

References in corpus (2)

• The weak Cartan property for the p-fine topology on metric spaces
• Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets

Cited by in corpus (5)

• Local and semilocal Poincaré inequalities on metric spaces
• Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces
• The Dirichlet problem for p-minimizers on finely open sets in metric spaces
• Convergence and local-to-global results for $p$-superminimizers on quasiopen sets
• The Perron method associated with finely $p$-harmonic functions on finely open sets