Quasiopen and p-Path Open Sets, and Characterizations of Quasicontinuity

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.