光滑纤维化的特征函数与诱导光滑纤维化

Characteristic Functions of Smooth Fibrations and Induced Smooth Fibrations

在差异空间范畴中研究了光滑纤维化与光滑上纤维化的等价刻画,利用光滑升腾函数与光滑收缩函数,分别证明了一个光滑映射是光滑纤维化的充要条件是其存在相应的光滑升腾函数、是光滑上纤维化的充要条件是其存在相应的光滑收缩函数.同时,证明了光滑纤维化或光滑上纤维化诱导的光滑映射空间之间的光滑映射是光滑纤维化.

The equivalent description of smooth fibration and smooth cofibration was studied in the category of di-ffeological spaces.By applying the smooth lifting function and the smooth retracting function,it was respectively shown that a smooth map is a smooth fibration if and only if it has a corresponding smooth lifting function and a smooth cofibration if and only if it has a corresponding smooth retracting function.Meanwhile,it was also shown that the smooth map between smooth mapping spaces induced by a smooth fibration or a smooth cofibration is again a smooth fibration.