中文摘要：

研究了取值收敛自由空间上的抽象函数的连续性、可微性与可积性，讨论了这一类函数的连续性、可微性和可积性与依坐标连续、可微和可积之间的关系，给出了与此有关的几个定理，并指出在λ=ω时定理的条件还可以进一步简化．

英文摘要：

The continuity, differentiability and integrality of abstract functions on convergence -free spaces are studied. The relationship between this class of abstract function＇ s continuity, differentiability, integrality in coordinates is discussed. Several theorem concerning this problem were presented. It is pointed out that the form of these theorems can be simplized when λ=ω