近似拓扑的并、交、补性质

The Properties of Union, Intersection and Complement Operators of Approximate Topology

引入拓扑的并、交、补拓扑,从而定义了近似拓扑的三种并、交、补结构,得出了对于近似拓扑的第三种并、交、补,近似拓扑具有封闭性和构成完备格,且近似算子是拓扑格到近似拓扑格的同态满射的重要结论.还研究了并、交、补拓扑在近似算子作用后与近似拓扑的并、交、补的重要关系.

In this paper, union, intersection and complement topologies of topology are introduced to define three kinds of union, intersection and complement structures for approximate topology. It is proved that for the third structure, the approximate topology is closed under the three operators and is a complete lattice. Moreover, it is also proved that the approximation operator is an epimorphism from topology lattice onto approximate topology lattice. Finally, some important relations are also studied between the union, intersection and complement topologies acted by the approximation operator and the union, intersection and complement of approximate topology.