拓撲完備集 的英文怎麼說
中文拼音 [tàpūwánbèijí]
拓撲完備集
英文
topologically complete set-
An important property of sobrification is given. by discussing the spectra of complete lattices, a theoretical foundation of sobrification of spaces is obtained. thus we know that the category of sober spaces is a reflective subcategory of the category of all the topological spaces with continuous functions
通過對完備格的譜理論的簡單討，為一般的拓撲空間及偏序集的sober匕做了理論上的鋪墊z指出了拓撲空間的sober化函子是從sob到top的包含函子的左拌隨，理想完備化函子是從alg到pos的遺忘函子的左拌隨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。With these concepts, the following results are obtained : ( 1 ) the set of compact elements in an algebraic l - domain is an l - cusl ; ( 2 ) algebraic l - domains equipped with scott topology are the soberification of their sets of compact elements equipped with pseudoscott topology ; ( 3 ) the ideal completion of an l - cusl is an algebraic l - domain, obtaining a representation theorem for algebraic l - domains
證明了：任一代數l - domain的緊元集是l - cusl ；任一代數l - domain是其緊元集賦予alexandrov拓撲時的sober化；任一l - cusl的理想完備化是代數l - domain ，從而得到了代數l - domain的表示定理。In feature description, a novel topological relationship set which is composed of six named topological relationships and an inverse operator is defined, and its completeness and exclusiveness are proved. then, a video shot model based on mpeg - 7 standard is constructed and a description scheme to video shot is implemented perfectly
在特徵描述與建模方面，提出了一種以六類拓撲關系組合逆運算符的新型拓撲關系集合，並證明了其具有完備性和互斥性，在此基礎上建立了一個基於mpeg - 7標準的視頻鏡頭模型，完整地實現了對視頻鏡頭的描述。分享友人