凝聚locale论文：Locale与拓扑空间的凝聚化.doc

凝聚locale论文：Locale与拓扑空间的凝聚化【中文摘要】在locale范畴或称为其对偶范畴的frame范畴的讨论和研究中,由于locale理论为拓扑学提供了一个重要的研究手段,在locale中完全从集合的开集开始谈论其性质,正是由于locale理论其研究拓扑结构的一种新的角度,也丰富和发展了拓扑学.一个范畴映射到另一范畴的函子,如果满足一些条件,定义它为扩张函子,对于扩张函子来说,它的相容性、饱和性、稳定性都是知道我们研究探讨的对象,本文主要研究对于凝聚范畴中的一些例子和关系.对于凝聚化这个扩张函子来说,它是相容饱和的；对于它的稳定性,这里给出了对象稳定的几个等价条件和充分条件,如谱T1和谱T2,对于拓扑结构稳定性的研究也给出了等价条件,如frame中的元是紧元,frame中每个理想是主理想.【英文摘要】In locale categories (or its dual category, the category of frame), discussion and research for topology locale theory provides an important research means-in the locale fully from the collection in the locale of open sets to its nature. For the study of the topological structure, a locale theory not only opened up a new perspective, but also enriches and develops the topology.A functor from a category mapped to another category, if meets some conditions, we can define it for expansion functor, for expansion overall functor compatibility and saturability, stability is all know we study object, this paper mainly studies for the some of the examples and relationship.For the expansion coherentily functor,it is compatible saturated; For its stability, this gives object stable several equivalent conditions and sufficient conditions such as prime T1 or prime T2; For the stability of the topological structure of the research also given conditions of equivalences, for example in a frame each element is compact or each ideal is principal ideal.【关键词】凝聚locale 凝聚化 扩张【英文关键词】coherent locale coherention expand【目录】Locale与拓扑空间的凝聚化摘要4-5Abstract5引言7-80.1 问题的提出7-80.2 文章结构81. 背景知识8-151.1 范畴相关的定义8-101.2 函子及其相关的概念10-152. 范畴FRM15-173. Loc点化和简要的结果17-204. 凝聚locale范畴和凝聚空间范畴的一些范畴性质20-244.1 凝聚空间的例子和性质20-214.2 Coh到Sp的包含映射i的范畴性质21-224.3 凝聚空间的几个等价条件22-245 扩张函子24-295.1 扩张函子25-265.2 相容扩张函子265.3 饱和扩张函子265.4 平稳函子26-275.5 凝聚空间的扩张函子27-29