The Weak Cartan Property for the p-fine Topology on Metric Spaces
نویسندگان
چکیده
We study the p-fine topology on complete metric spaces equipped with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. We establish a weak Cartan property, which yields characterizations of the p-thinness and the p-fine continuity, and allows us to show that the p-fine topology is the coarsest topology making all psuperharmonic functions continuous. Our p-harmonic and superharmonic functions are defined by means of scalar-valued upper gradients and do not rely on a vector-valued differentiable structure.
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