# completely distributive lattice中文翻譯

• 完全分配格
###### 例句與用法
• A note on generalized completely distributive lattices
關于廣義完全分配格的一個注記
• Characterization of completely distributive lattices
完全分配格的刻劃
• 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 ]
這一定理已經被以多種形式推廣，其中主要有兩個方向，一個是用具有某種可數性的完全分配格來代替插入定理中的實數空間r ，即劉應明和羅懋康在他們合寫的文[ 6 ]中就嘗試在格上定義模糊拓撲空間的正規性，并得到了一系列很好的結果。
• 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
構造性地給出一對函子，并以此證明了范疇stml ( l )的一個表示定理，即范疇stml ( l )與范疇fsts ( l ) (由l - fuzzifyingscott拓撲空間與保定向并和way - below關系的l - fuzzifying連續映射所構成的范疇)等價。
• 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擬序集上定義廣義alexandroff拓撲，證明了它是通常擬序集上alexandroff拓撲的推廣，一個l - fuzzy擬序集( x ， e )上的廣義alexandroff拓撲可以由其上一族alexandroff拓撲取并得到，任意一個拓撲空間的拓撲都可以表示為某個l - fuzzy擬序集上的廣義alexandroff拓撲，以及l - fuzzy擬序集上的廣義alexandroff拓撲是j . j . m . m . rutten等定義的廣義超度量空間上廣義alexandroff拓撲的推廣。 ( 2 )通過引入l - fuzzy偏序集上的l - fuzzy集關于l - fuzzy偏序的并以及l - fuzzy擬序集上(關于l - fuzzy擬序)的l - fuzzy定向集等概念，定義了l - fuzzy定向完備的l - fuzzy偏序集(簡稱l - fuzzydcpo ，又叫l - fuzzydomain )和l - fuzzyscott連續映射，證明了它們分別是通常的dcpo和scott連續映射的推廣，當l是帶有逆序對合對應的完全分配格時，以l - fuzzydomain為對象， l - fuzzyscott連續映射為態射的范疇l - fdom同構于一類特殊的v - domain范疇，即以定向完備的l -值擬超度量空間為對象， scott連續映射為態射的范疇l - dcqum ，以及當l是1為分子的完全分配格時， l - fuzzydomain和l - fuzzyscott連續映射一致于k . wagner在[ 59 ]中定義的定向liminf完備的-范疇和liminf連續映射。
• ( 4 ) we construct the concepts of stratified approximations and base in an l - fuzzy domain , and define uniformly continuous l - fuzzy domain and algebraic l - fuzzy domain by means of the concept of base for l - fuzzy domain , prove that they are generalizations of ordinary continuous domain and algebraic domain , when l is a completely distributive lattice in which 1 is a molecule and the minimal mapping on l preserves finite meet , the stratified approximation relations on a continuous l - fuzzy domain satisfy the property of stratified interpolations , and is consist of a base for the generalized scott topology on a continuous l - fuzzy domain ( x , e ) , and every continuous l - fuzzy domain can be seen as an l - fuzzy scott continuous retraction of some algebraic l - fuzzy domain
( 4 )在l - fuzzydomain中引進層次逼近和基的概念，用統一的基的方法定義了連續l - fuzzydomain和代數l - fuzzydomain ，證明了它們分別是通常的連續domain和代數domain的推廣。當l是1為分子的完全分配格，并且其上的極小映射保有限交時，證明了連續l - fuzzydomain上的層次逼近關系滿足層次插值性質，構成連續l - fuzzydomain ( x ， e )上廣義scott拓撲的基，以及任意的連續l - fuzzydomain都可以作為某代數l - fuzzydomain的l - fuzzyscott連續收縮。

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