连续函数图象的研究因其重要的理论意义以及应用价值而备受关注。许多令人感兴趣的分形常以函数图象的形式出现的。关于函数图象有关分形维数的普适性质，函数图象关于维数的分解问题在近几十年引起国内外学者极大地研究兴趣。.在我们已有工作的基础上，本项目拟以分形维数为主要工具，主要探讨以下两个问题：1.利用分形维数考虑紧空间上连续函数图象的k-普适性问题；2.连续函数图象的分解问题。.我们将结合测度论，分形几何，空间理论的技巧和方法为具体的连续函数图象的分形维数的计算提供新的方法。呈现和刻画连续函数空间有关图象分形维数的普适性质，进一步丰富函数空间的分形维数理论。

The research on fractal properties of graphs of continuous functions is one of the hot topic in fractal geometry.A variety of interesting fractals,both of theoretical and practical importance,occur as graphs of functions. In recent decades,there has a large interesting in study dimensions of various sets related to generic continuous functions, such as graphs of continuous functions,as well as the decomposition problems of the continuous functions..On the basis of our preceding works,and using fractal dimensions as the main tools,we study the following subjects in this project:(1)the k-prevalent properties of the graphs for continuous functions on a compact space,(2)the study of decomposition of graphs for continuous functions in terms of various fractal dimensions..Combing techniques from measure theory,fractal geometry and compact space theory,we will provide new methods to determine the fractal dimensions of graphs,and we shall present and characterize the generic properties of the graphs in more details to enrich the dimension theory of the function spaces.