导算子保并的定理和不保并的反例

A theorem and example of preserving union and not presering union in derived operator

研究了L fuzzy拓扑空间中T-1分离性与导算子保并性的关系 ,证明了在菱形格上的拓扑空间中T-1分离性是导算子保并的充分条件 ,同时给出了在一类六元格上的拓扑空间中T-1分离性不能保证导算子保并性的反例 .这个结果回答了导算子在一般T-1的L fuzzy拓扑空间中是否保并这一公开问题 .

The relation was studied between T -1 seperation and derived operator preserring union in a L fuzzy topological space. The theorem that derived operator preserre union in a T -1 topolopical space on a diamond lattice was proved. Moreorer, conterexample of derived operator not preserving union was mede in a T -1 topological space on a six element lattice. These results answered the open problem whether derived operator preserve finite union in a T -1 L fuzzy topological space.