A new Cartan-type property and strict quasicoverings when p=1 in metric spaces

Original · EN

In a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality, we prove a new Cartan-type property for the fine topology in the case p=1. Then we use this property to prove the existence of 1-finely open strict subsets and strict quasicoverings of 1-finely open sets. As an application, we study fine Newton-Sobolev spaces in the case p=1, that is, Newton-Sobolev spaces defined on 1-finely open sets.