topological lattice 中文意思是什麼

Closeness of product and coproduct operation inseveral kinds of the category of lattice - valued topological spaces

幾種格上拓撲空間范疇中乘積與上積運算的封閉性

These theorems show the inherent relation between - smooth pointwise quasi - uniformity and point - wise quasi - uniformity. it is proved that every - smooth topological molecular lattice is stratum pointwise quasi - uniformizable, and - smooth pointwise quasi - uniformizable if it satisfies some conditions, every - smooth pointwise quasi - uniformity can induce an - smooth co - topology if it satisfies some conditions

證明了每個l - smooth拓撲分子格都可以層點式擬一致化，在一定條件下可l - smooth點式擬一致化，每個l - smooth點式擬一致結構在一定條件下可以誘導出一個l - smooth余拓撲。

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。

In the second chapter, the lattice - valued fuzzy sets have been introduced si mply, furthermore, the vertion of ( monotone ) insrtion theorem on lattice in fuzzy topological space have been shown

第二章簡單介紹了格值模糊集，且進一步給出格上（單調）插入定理在l -模糊拓撲空間中的表現形式。

In the first part, the concept of lattice valued smooth topological molecular lattice and its category are researched

本文由兩部分組成，第一部分是關于格值smooth拓撲分子格及其范疇的研究。

In this paper, our main purpose is to build a concept of lattice valued smooth topological molecular lattice, to research related properties of its category, and to study the fuzzy paracom - pactness and connectness in the l - topological spaces. this paper is consist of two part. there are four chapters

本文的主要目的是在拓撲分子格理論的基礎之上建立格值smooth拓撲分子格理論的基本框架，研究格值smooth拓撲分子格範疇的相關性質，並對l -拓撲空間中fuzzy仿緊性和連通性等問題作深入地研究。

As the layer structure of lattice, relative separation properties and relative compactness in l - fuzzy topological spaces are more complex than that in general topological spaces

由於層次結構的存在， l - fuzzy拓撲空間中的相對分離性和相對緊性較一般拓撲學中的相對分離性與相對緊性復雜得多。