category of topological spaces 中文意思是什麼

category of topological spaces 解釋
拓撲空間的范疇
  • category : n. 1. 類型，部門，種類，類別；類目。2. 【哲、邏】范疇。3. 〈pl. 〉體重等級。
  • of : OF ＝Old French 古法語。
  • topological : 拓撲的
  • spaces : 控制室
  1. 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
  2. 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
  3. This paper defines homology monomorphism, homology epimorphism, homology regular morphism in the category of topological spaces with point by using homology functor

    摘要利用同調函子，在點標拓撲空間范疇中定義了同調單態、同調滿態、同調正則態射等概念。
  4. 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。
  5. By constructing two functor, we have proved a representation theorem of the category stml that the category stml is equivalent with the category fsts, where fsts is consisted of - fuzzifying scott topological spaces and the mappings which are preserving directed - join and way - below relation and continuous. besides, the category stml ( c ) has been discussed, where c is a subcategory of the category of the completely distributive lattices and gohs, c, morphisms are ( 1, 2 ) - smooth continuous goh

    構造性地給出一對函子，並以此證明了范疇stml （ l ）的一個表示定理，即范疇stml （ l ）與范疇fsts （ l ） （由l - fuzzifyingscott拓撲空間與保定向並和way - below關系的l - fuzzifying連續映射所構成的范疇）等價。
  6. 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。
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