Characteristic Functions of Smooth Fibrations and Induced Smooth Fibrations

ZHAN Yan; ZHAO Hao

doi:10.6054/j.jscnun.2021013

Journal of South China Normal University (Natural Science Edition) > 2021 > 53(1): 85-89. > DOI: 10.6054/j.jscnun.2021013

ZHAN Yan, ZHAO Hao. Characteristic Functions of Smooth Fibrations and Induced Smooth Fibrations[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(1): 85-89. DOI: 10.6054/j.jscnun.2021013

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Characteristic Functions of Smooth Fibrations and Induced Smooth Fibrations

ZHAN Yan,
ZHAO Hao^,

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

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Received Date: September 23, 2020
Available Online: March 23, 2021

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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.
- diffeological space,
- smooth fibration,
- smooth cofibration

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