【作者】 陶波；

【导师】 周武能；

【作者基本信息】 浙江师范大学 ， 基础数学， 2004， 硕士

【摘要】 本文第一部分首先利用相关远域族的概念引入L-拓扑空间中的*超仿紧性，讨论了它的基本性质以及它与其它仿紧性的关系，并得到其闭遗传、弱同胚不变、L-好的推广以及加强T₂分离性等诸多好的性质。文中还得到了*超仿紧性的子基引理，并且利用*超仿紧性中证明子基引理的方法证明了其它各种仿紧性的子基引理。 第二部分研究了相关远域族的另一个应用，即建立了近似超紧性。它是L-拓扑空间中超紧性的推广。这部分讨论近似超紧性与超紧性以及近似良紧性之间的关系，并且证明了它具有正则闭遗传、有限可和以及弱拓扑不变等性质并且得到近似超紧性的子基引理和乘积定理。同时，文中也对近似超紧性进行了网式和滤子式刻划。 本文的第三部分利用L-拓扑空间中的另一种LF集-半闭集介绍了S_L-闭包空间，指出它是L-拓扑空间中S-闭包算子的推广，并研究它的收敛性。文中提出S_L-连续映射的概念并讨论它的性质和特征。本文还以S_L-闭包空间为对象，S_L-连续映射为态射建立了S_L-闭包范畴S_L-CLOSURE，研究这种结构的性质，得到了它是集范畴SET上相对于忘却函子T_S：S_L-CLOSURE→SET的一个拓扑范畴。本文最后还得到了函子ω_L^S和ι_L^S是互为伴随的这一重要定理。更多还原

【Abstract】 In the first section of this paper, a new kind of paracompactness based on the concept of relative remote neighborhood family in L-topological spaces is established. The relationships between this paracompactness and the other paracompactnesses are discussed. Many properties such as L-good extension, hereditary with respect to closed subsets, weakly topological property and strenthening T2 seperated properties are gotten. And in this section, the sub-base lemma in *-ultra-paracompactness is proved and the subbase lemmas of the other paracompactnesses are also proved by means of the method used in *-ultra-paracompact spaces.In the second section, another application of relative remote neighborhood family is researched. The nearly ultra-fuzzy compactness is generalization of ultra-fuzzy compactness in L-topological spaces. The relationships between this compactness and the other compactness are discussed. It possesses many the properties such as hereditary with respect to regular closed subsets, weakly topoligical property, the subbase lemma and the product theorem. At the same time, the characterizations of the nearly ultra-fuzzy compactness by filters and nets are introduced.In the third section, the concept of SL-closure space is introduced by another LF-set, i.e. semi-closed set. It is a generalization of S-closure operator in L- topological spaces. In this section, its convergence is studied and the SL-continuous generalize order homomorphisms are introduced. The properties and characters of the morphism are gotten. Furthermore, the categorySl-CLOSURE is established and its structure is studied. Some important results, for example Sl-CLOSURE is a topological category over SET w.r.t.Ts where Ts : SL-CLOSURE SET is a forgetful functor, are obtained. At last, the theorem that the functor wSL is the left-adjoint of the functor lSL is proved .更多还原