%0 Journal Article %T The weak Cartan property for the p-fine topology on metric spaces %A Anders Bj£¿rn %A Jana Bj£¿rn %A Visa Latvala %J Mathematics %D 2013 %I arXiv %X We study the p-fine topology on complete metric spaces equipped with a doubling measure supporting a p-Poincare inequality, 1 < p< oo. 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 p-superharmonic 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. %U http://arxiv.org/abs/1310.8101v1