中文摘要：

本文对函数空间在集开拓扑下的不变余度量性质进行了推广，给出了函数空间在紧开拓扑和点收敛拓扑下不变余度量化的充要条件．

英文摘要：

A generalization of the invariantly cometrizable property is given for the set-open topology for function spaces. And the sufficiency and necessity condition of a function space to be invariantly cometrizable in the compact-open and point-wise convergence topology is given as a corollary.