ultrametric造句

• 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。
• 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。