English translation for "alexandroff"

亚历山德罗夫

Example Sentences:

	1.	In order to prove the arbitrary cardinal number alexandroff - urysohn addition theorem put forward in 1923 , the famous former soviet union topologist a . arhangel ' skii introduced network which is the important extension of base in 1959 1959年前苏联著名拓扑学家a arhangel ' skii为了证明1923年提出的任意基数的alexandroff - urysohn加法定理，引进了基概念的重要推广? ?网络( network ) 。
	2.	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。
	3.	On the other hand , locally finite families introduced by p . alexandroff in 1924 have played a fundamental role in the research of metrization problem and paracompact property . research of space with - locally finite networks betters understanding of metric property ' s essence . hereditarily closure - preserving families introduced by n . lasnev in 1966 ties up locally finite families Alexandroff引入的局部有限集族( locallyfinitefamilies )已在度量化问题及仿紧性的研究中起着不可替代的作用，对于具有局部有限网络空间的探索更加深了人们对度量性的本质了解， 1966年n

Similar Words：

"alexandrium" English translation, "alexandro" English translation, "alexandro jodorowsky" English translation, "alexandroae" English translation, "alexandroaie" English translation, "alexandrolite" English translation, "alexandropoulos" English translation, "alexandros" English translation, "alexandros akrivakis" English translation, "alexandros baltas" English translation