关于单纯逼近的定义与Croom商榷

ON THE DEFINITION OF THE SIMPLICIAL APPROXIMATION——A DISCUSSION WITH CROOM

将 Croom 关于多面体之间的连续映射的单纯逼近的定义与一般通常采用的定义进行比较,指出这2种定义是不等价的,由于 Croom 的定义减弱了条件,不要求满足星形性质,因而不能反映“逼近”的程度,致使应用该定义时不得不补足条件.

Making a comparison of Croom's definition of the simplicial approximation of a continuous map between polyhedrons with the definition in common use,it is pointed out that these two defintions are nonquivalent. As the condition is weakened in Croom's definition which does not require to satisfy the star property,the approximation degree connot be reflected and consequently additional condition has to be supplemented when this defini- tion is applied.