内部算子与内部算子格

Inner Operator and Inner Operator Lattice

本文通过对拓扑空间上的内部算子及其性质的研究,给出了同一集合上的内部算子之间的偏序关系,重新定义了同一集合上的内部算子在此偏序关系上的交与并运算,并构造出同一集合上的内部算子关于此偏序关系的上下确界,进而得到了完备的内部算子格.

In this paper,we first study the inner operator and its properties on topology space.Then,we give the partially order between the two inner operators on the given set.With the order,we redefine the meet and join of inner operators on the given set and give the least upper bound and the greatest lower bound of them.At the last,we obtain the complete inner operator lattice.