Diffeological空间范畴中光滑映射的分解  

DECOMPOSITIONS OF SMOOTH MAPS IN DIFFEOLOGICAL SPACE CATEGORY

作　　者：詹妍[1] 赵浩[1] ZHAN Yan;ZHAO Hao(School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China)

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《数学杂志》2021年第3期237-246,共10页Journal of Mathematics

基　　金：国家自然科学基金面上项目资助(11671154,11761072);广东省自然科学基金面上项目资助(2020A1515011008).

摘　　要：本文研究了diffeological空间范畴中光滑映射的分解问题.利用经典同伦论中映射分解的方法,获得了任何一个光滑映射都可以分解为一个光滑同伦等价和光滑纤维化或光滑上纤维化的复合的结果,推广了拓扑空间范畴中的相关结果.In this paper we study the decomposition problem of smooth maps in the diffeological space category.We apply the method of decomposition of maps from the classical homotopy theory to show that any smooth map can be decomposed as the composition of a smooth homotopy equivalence with a smooth fibration or a smooth cofibration.It generalizes the related results in the topological space category.

关 键 词：diffeological空间 光滑纤维化 光滑上纤维化 

分 类 号：O189[理学—数学]