一类复合函数的弧式连通性

Arcwise Connectedness for a Class of Compound Functions

本文在较弱的假设下，讨论了形如Φ（ｘ）＝ｆ（ｘ），ｇ（ｘ））（其中ｆ：Ｒｎ→Ｒｍ，ｇ：Ｒｎ→Ｒｋ，：Ｒｍ×Ｒｋ→Ｒ）的一类复合函数的弧式连通性和广义弧式连通性。

In this paper,under weak assumptions,arcwise connectedness and several classes of generalized arcwise connectednesses are discussed and proved for aclass of compound functions (x)=(f(x), g(x))(Where f:Rn→Rm,g:Rn→Rk,:Rm ×Rk→R).