The Sun Topology and a-fine Topologies in the Plane

In 1999 P. Pyrih proved that the sun topology is strictly finer than the fine topology from the logarithmic potential theory in the plane. In our paper it is proved that the sun topology is strictly finer that a-fine topology when 1a2, from Riesz potential theory. And from our conclusions and the known results follows the strictly conclusion relation formula: The sun topology a-fine topology fine topology Euclid topology.