关于完备格成分理论中两个问题的探讨

研究了完备格成分理论中两个尚未解决的问题：（i)在非分配的完备格中，有限宽元素的成分也是有限宽的吗？（ii)什么样的映射能保持颗粒表示性质或颗粒性质？通过构造反例证明了在非分配的完备格中，有限宽元素的成分不必是有限宽的；还证明了完备格间的同构映射能保持颗粒表示性质和颗粒性质，通过反例证明了同构映射的条件不能减弱，从而解决了以上两个问题。

Solutions to two problems in component theory of complete lattices

The following two open problems in the component theory of complete lattices are studied: (1) In a non distributive complete lattice, is it true that any component of an element with finite width is also finite wide? (2) What functions between complete lattices can preserve the granule representable property or granule property? Through constructing a counterexample it is showed that there is a non distributive complete lattice in which a component of some element with finite width is not finite wide. Furthermore, it is showed that an isomorphism between complete lattices can preserve the granule representable property and granule property, and counterexamples are given to show that the condition of isomorphism can not be weakened. So the two open problems list above are completely solved.