In this note,the author gives some characterizations of regularity and complete regularity of topological molecular lattices,the shows that any regular and strong normal topological molecular lattice is completely reg...In this note,the author gives some characterizations of regularity and complete regularity of topological molecular lattices,the shows that any regular and strong normal topological molecular lattice is completely regular;finally proves that every paracompact and regular topological molecular lattics is stronge normal,and further completely regular.展开更多
In this paper,we first give out a new characterization of continuous lattices,then,by using the similarity between continuous lattices and com- pletely distributive lattices,we give out a similar characterioation of c...In this paper,we first give out a new characterization of continuous lattices,then,by using the similarity between continuous lattices and com- pletely distributive lattices,we give out a similar characterioation of com- pletely distributive lattices.Finally,we give out a categorical theorem on completely distributive lattices.展开更多
In this paper, we discuss some propertie s of lattice implication algebra and difine the transitivity of implication in a set, we show the transitivity of implication and the substitution Theorem hold i n filters. S...In this paper, we discuss some propertie s of lattice implication algebra and difine the transitivity of implication in a set, we show the transitivity of implication and the substitution Theorem hold i n filters. So every filter of lattice implication algebra satisfies the Syllogis m and substitution Theorem of propositional logic.展开更多
文摘In this note,the author gives some characterizations of regularity and complete regularity of topological molecular lattices,the shows that any regular and strong normal topological molecular lattice is completely regular;finally proves that every paracompact and regular topological molecular lattics is stronge normal,and further completely regular.
文摘In this paper,we first give out a new characterization of continuous lattices,then,by using the similarity between continuous lattices and com- pletely distributive lattices,we give out a similar characterioation of com- pletely distributive lattices.Finally,we give out a categorical theorem on completely distributive lattices.
文摘In this paper, we discuss some propertie s of lattice implication algebra and difine the transitivity of implication in a set, we show the transitivity of implication and the substitution Theorem hold i n filters. So every filter of lattice implication algebra satisfies the Syllogis m and substitution Theorem of propositional logic.
