Diffeological空间范畴中光滑映射的分解

DECOMPOSITIONS OF SMOOTH MAPS IN DIFFEOLOGICAL SPACE CATEGORY

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.