平面上的太阳拓扑与α-细拓扑

The Sun Topology and a-fine Topologies in the Plane

本文证明了平面上的太阳拓扑严格细于关于Riesz位势论的细拓扑(即a-拓扑,1< a<2 ),从而得到了如下严格包含关系式: 太阳拓扑a-细拓扑2-细拓扑欧氏拓扑。

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 1<a<2, 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.