partial directed set 中文意思是什麼
partial directed set
解釋
部分有向集-
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拓撲取並得到，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偏序的並以及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同構於一類特殊的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連續映射一致於k . wagner在[ 59 ]中定義的定向liminf完備的-范疇和liminf連續映射。
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