几类映射与广义纤维拓扑范畴的分离性
Some Mappings and the Separation Properties of the Fibrewise Topology Category
【中文摘要】 纤维分离条件在TOPB范畴(对象是以B为基底的纤维拓扑空间( X ,p), (Y ,q),态射是X到Y的连续映射φ且满足qφ=p)中占有重要地位。在TOPB范畴中两个对象之间的分离性如何保持(逆保持)与态射φ的选择有直接关系。本文在结合TOPB范畴中已有性质的基础上,主要是对TOP?范畴(对象是( X ,p,B)(Y,q,D),态射是连续偶(φ,λ),λp =qφ)中两个对象之间的分离性如何保持(逆保持)而做出的推广,引入并讨论了三种对于保持(逆保持)分离性有很好的性质的映射。主要内容有:1、积投射在底空间之间,纤维拓扑空间之间时对TOP*范畴的纤维R 0性,纤维Ti (i =0,1,2.)性,纤维(完全)正则性,纤维(函数)正规性的一些保持(逆保持)分离性的性质。2、有限对一映射在纤维拓扑空间中对纤维R 0性的一些保持(逆保持)分离性的性质。3、完全纤维映射在纤维拓扑空间中对纤维正则性等的一些保持(逆保持)分离性的性质。

【英文摘要】 The fibrewise separates condition holds important status in the TOPB category (the objects are the fibrewise topological spaces over B ,for two objects ( X ,p), (Y ,q), ,a morphism from X to Y is a contimuous map such that qφ=p.How to preserves the separation properties between two objects of TOPB category have direct effect with the morphismφ. Combined properties with having listed properties of TOPB category , This thesis will mianly generalize the separates properties preserves (inversely preserves) which between in the two already objects of TOP? category (the objects are ( X ,p,B)and(Y,q,D), the morphismis a contimuous pair of (φ,λ),which s.tλp = qφ. we will draw in and discuss three mappings which have good properties about preserves (inversely preserves) separation properties,Main content has:1, How the product map preserves (inversely preserves) fibrewise R 0 ,fibrewise Ti (i =0,1,2.),fibrewise (completely) regular , fibrewise (functionally) normal properties of TOPB category when it exist between base spaces or fibrewise topology spaces .2, The limited to one map preserves (inversely preserves) fibrewise R0 of TOPB category between in fibrewise topology spaces .. 3 , The completely fibrewise map preserves (inversely preserves) fibrewise normal propertiy of TOPB category between in fibrewise topology spaces. 

【中文关键词】 TOPB范畴; TOP*范畴; 纤维R0性; 纤维Ti (i =0; 1; 2.)性; 纤维(完全)正则性; 纤维(函数)正规性; 积投射; 有限对一映射; 完全纤维映射
【英文关键词】 TOPB category ; TOP* category ; fibrewise R0; fibrewise Ti(i =0; 1; 2.); fibrewise (completely) regular; fibrewise (functionally) normal; the product map; The limited to one map; The completely fibrewise map
【毕业论文目录】
摘要 4-5
Abstract 5
1. 前言 7-8
    1.1 问题的提出 7-8
    1.2 文章结构与简介 8
2. 预备知识 8-15
3. 积投射与TOP_* 范畴的纤维分离性 15-26
    3.1 积投射的性质及其与TOP_* 范畴的一些性质 15-18
    3.2 积投射与TOP_* 范畴的纤维R_0 性 18-19
    3.3 积投射与TOP_* 范畴的纤维T_i(i =0,1, 2.) 性 19-21
    3.4 积投射与TOP_* 范畴的纤维（完全）正则性 21-23
    3.5 积投射与TOP_* 范畴的纤维（函数）正规性 23-26
4. 有限对一映射与TOP_* 范畴的纤维分离性 26-28
    4.1 有限对一映射的性质 26-27
    4.2 有限对一映射与TOP_* 范畴的纤维分离性 27-28
5. 完全纤维映射与TOP_* 范畴的纤维分离性 28-30
参考文献 30-31
致谢 31