论文标题:L-拓扑空间的局部仿紧性及δ-连通性
Local Paracompactness and δ-connectedness in L-topological Spaces
论文作者
论文导师 李生刚,论文学位 硕士,论文专业 基础数学
论文单位 陕西师范大学,点击次数 114,论文页数 38页File Size1348K
2006-04-01论文网 http://www.lw23.com/lunwen_369909752/
Topological spaces;Locally compact spaces;Locally Paracompactspaces;L—topological spaces;Local N—compactness;Local Paxacompactness;Flattice;Connectedness;δ—connectedness;δ—connected component
本文以拓扑空间的局部紧性、L-拓扑空间的局部良紧性以及连通性为基础,研究拓扑空间的局部仿紧性、L-拓扑空间的局部仿紧性以及δ-连通性。主要内容如下: 第一章 作为预备部分,给出了全文将要用到的一些概念、符号和结果。 第二章 给出了拓扑空间的三种局部仿紧性的定义,证明了这三种局部仿紧性在正则空间范畴中是等价的;分别讨论了它们对开、闭子空间的遗传性、在连续的既开又闭映射下的不变性以及可和性等;证明了这三种局部仿紧性均可加强分离性。 第三章 给出了L-拓扑空间的六种局部仿紧性的定义,研究了这六种局部仿紧性之间的蕴涵关系,证明了本文第二章所定义的拓扑空间的局部仿紧性的一些重要结果对局部仿紧L-拓扑空间仍成立,并将局部良紧L-拓扑空间的某些好的性质推广到相应的局部仿紧L-拓扑空间。结果表明前四种局部仿紧性既是闭遗传的又是开遗传的,后两种局部仿紧性是闭遗传的。这些局部仿紧性在某种序同态下是保持不变的。 第四章 研究了L-拓扑空间的δ-连通性。定义了L-拓扑空间的δ-连通性和δ-连通分支的概念,讨论了它们的一些性质,给出δ-连通的一些等价刻画,证明了δ-连通L-拓扑空间是比连通L-拓扑空间更广泛的一类空间。在F格L的最大元1是分子时,得到了δ-连通性是可积性质的结论。作为特例,I-单位区间和I-实直线是δ-连通的。
In this paper, based on local compactness in topological spaces, local N-compactness and connectedness in L—topological spaces, we have studied local paxacompactness in topological spaces, local paxacompactness and δ—connectedness in L—topological spaces. The main content of this paper is as follows:In Chapter 1, preparation knowledge, defines some notions and gives some symbols and theorems we will use in this paper.In Chapter 2, three kinds of local paxacompactness axe defined. It is proved that the three kinds of local paracompactnesse are quivalent in the case of regular, and their properties axe discussed respectively. It is shown that they axe hereditary for both open subspaces and closed subspaces. Versions of some other classical properties of local paxacompactness are obtained.In Chapter 3, six kinds of local paracompactnesses in L—topological spaces axe given, and implication relations among them are studied. Some good properties of local paxacompactness which is given in chapter 2 in topological spaces axe generalized to locally paracompact L—topological spaces, and some good properties in locally N-compact L—topological spaces axe extended to locally paracompact L—topological spaces. It is proved that the first four kinds of local paracompactnesses are inherited by closed subspaces and open subspaces, the last two kinds of local paracompactnesses are inherited by closed subspaces. It is abtained that these local paracompactnesses are invariable under some order homomorphism.In Chapter 4, we have studied δ—connectedness in L—topological spaces. δ— connectedness and δ—connected component are denned. Some properties and equivalent conditions about δ—connected axe given. It is respectively discussed that δ—connected L—topological spaces are abroader than connected L—topological spaces. Especially some interesting conclusions axe obtained when maximum of Flattice L is molecular, it is proved that δ—connectedness is productive. As an example, the I-unit interval and the I-real line are δ—connected.
|
