关于覆叠同伦正则态射  

On covering homotopy regular morphisms

作　　者：陈淑萍[1] 钱有华[2] 

机构地区：[1]台州学院数学与信息工程学院,浙江临海317000 [2]浙江师范大学数理学院,浙江金华321004

出　　处：《宝鸡文理学院学报（自然科学版）》2006年第4期269-272,共4页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：浙江师范大学青年基金项目(20042053)

摘　　要：目的在点标道路连通CW空间的同伦范畴中，引进覆叠同伦正则态射的概念，研究它存在的条件、性质以及它与覆叠同伦单（满）态和覆叠同伦等价之间的关系。方法利用万有覆叠函子，将映射f：X→Y的研究转化为对它在万有覆叠空间上诱导的映射f：X（0）→Y（0）进行研究。结果推广了同胚映射、同伦等价和同伦正则态射的有关结果。结论若f为同伦正则态射,则f必为覆叠同伦正则态射；若f为覆叠同伦正则态射，则f不一定是同伦正则态射。Aim To define covering homotopy regular morphism in the homotopy category of pointed path-connected CW-spaces. To discuss its existence conditions, properties and the close relationships to covering homotopy monomorphism （epimorphism） and covering homotopy equivalence. Methods The studies on the map f： X → Y are transfered to the studies on the map f：X（0） → Y（0） that is induced by universal covering spaces by using universal covering functor. Results Generalizing some results of homeomorphic morphism, homotopy equivalence and homotopy regular morphism. Conclusion The map f is a covering homotopy regular morphism if it is a homotopy regular morphism; The map f is not surely a homotopy regular morphism if it is a covering homotopy regular morphism.

关 键 词：覆叠同伦单态 覆叠同伦满态 覆叠同伦正则态射 覆叠同伦标准分解 

分 类 号：O189.2[理学—数学]