completely distributive lattice meaning in English
完全分配格
Examples
- A note on generalized completely distributive lattices
关于广义完全分配格的一个注记 - Characterization of completely distributive lattices
完全分配格的刻划 - This theorem have been generalized in many ways . there are mostly two aspects in them , one is replacing the space r in insertion theorem by completely distributive lattices with some countability , i . e . , liu and luo in [ 6 ] try to use lower ( upper ) semicontinuous map well defined to define the normality of fuzzy topol ogical space and gain a series of good results [ 6 ]
这一定理已经被以多种形式推广，其中主要有两个方向，一个是用具有某种可数性的完全分配格来代替插入定理中的实数空间r ，即刘应明和罗懋康在他们合写的文[ 6 ]中就尝试在格上定义模糊拓扑空间的正规性，并得到了一系列很好的结果。 - By constructing two functor , we have proved a representation theorem of the category stml that the category stml is equivalent with the category fsts , where fsts is consisted of - fuzzifying scott topological spaces and the mappings which are preserving directed - join and way - below relation and continuous . besides , the category stml ( c ) has been discussed , where c is a subcategory of the category of the completely distributive lattices and gohs , c , morphisms are ( 1 , 2 ) - smooth continuous goh
构造性地给出一对函子，并以此证明了范畴stml ( l )的一个表示定理，即范畴stml ( l )与范畴fsts ( l ) (由l - fuzzifyingscott拓扑空间与保定向并和way - below关系的l - fuzzifying连续映射所构成的范畴)等价。 - The primary studies in this paper are the following : ( 1 ) we define a generalized alexandroff topology on an l - fuzzy quasi ordered set which is a generalization of the alexandroff topology on an ordinary quasi ordered set , prove that the generalized alexandroff topology on an l - quasi ordered set ( x , e ) can be obtained by the join of a family of the alexandroff topologies on it , a topology on any topological space can be represented as a generalized alexandroff topology on some l - quasi ordered set , and the generalized alexandroff topologies on l - fuzzy quasi ordered sets are generalizations of the generalized alexandroff topologies on generalized ultrametric spaces which are defined by j . j . m . m . rutten etc . ( 2 ) by introducing the concepts of the join of l - fuzzy set on an l - fuzzy partial ordered set with respect to the l - fuzzy partial order and l - fuzzy directed set on an l - fuzzy quasi ordered set ( with respect to the l - fuzzy quasi order ) , we define l - fuzzy directed - complete l - fuzzy partial ordered set ( or briefly , l - fuzzy dcpo or l - fuzzy domain ) and l - fuzzy scott continuous mapping , prove that they are respectively generalizations of ordinary dcpo and scott continuous mapping , when l is a completely distributive lattice with order - reversing involution , the category l - fdom of l - fuzzy domains and l - fuzzy scott continuous mappings is isomorphic to a special kind of the category of v - domains and scott continuous mappings , that is , the category l - dcqum of directed - complete l - quasi ultrametric spaces and scott continuous mappings , and when l is a completely distributive lattice in which 1 is a molecule , l - fuzzy domains and l - fuzzy scott continuous mappings are consistent to directed lim inf complete categories and lim inf co ntinuous mappings in [ 59 ]
本文主要工作是： ( 1 )在l - fuzzy拟序集上定义广义alexandroff拓扑，证明了它是通常拟序集上alexandroff拓扑的推广，一个l - fuzzy拟序集( x ， e )上的广义alexandroff拓扑可以由其上一族alexandroff拓扑取并得到，任意一个拓扑空间的拓扑都可以表示为某个l - fuzzy拟序集上的广义alexandroff拓扑，以及l - fuzzy拟序集上的广义alexandroff拓扑是j . j . m . m . rutten等定义的广义超度量空间上广义alexandroff拓扑的推广。 ( 2 )通过引入l - fuzzy偏序集上的l - fuzzy集关于l - fuzzy偏序的并以及l - fuzzy拟序集上(关于l - fuzzy拟序)的l - fuzzy定向集等概念，定义了l - fuzzy定向完备的l - fuzzy偏序集(简称l - fuzzydcpo ，又叫l - fuzzydomain )和l - fuzzyscott连续映射，证明了它们分别是通常的dcpo和scott连续映射的推广，当l是带有逆序对合对应的完全分配格时，以l - fuzzydomain为对象， l - fuzzyscott连续映射为态射的范畴l - fdom同构于一类特殊的v - domain范畴，即以定向完备的l -值拟超度量空间为对象， scott连续映射为态射的范畴l - dcqum ，以及当l是1为分子的完全分配格时， l - fuzzydomain和l - fuzzyscott连续映射一致于k . wagner在[ 59 ]中定义的定向liminf完备的-范畴和liminf连续映射。