中文摘要：

令C_β为压缩率为β∈（0,1/3）的齐次三部分Cantor集.本文研究一个可视性问题：对给定的β∈（0,1/3）,考虑是否存在过原点（0,0）斜率为λ的射线L_λ（λ∈（0,1））,使得其与集合C_β×C_β相交仅仅包含原点.利用重正规化方法得到了一些结果.

英文摘要：

Let C_βbe the three-part homogenous cantor-set with ratioβ∈（0,1/3）.Thispaper studied a visibility problem：givenβ∈（0,1/3）,is there a ray L_λwith slopeλ∈（0,1）which goes through the origin（0,0）such that the intersection of L_λand set（C_β×C_β）only contains the origin？ Based on the method of renormalization,some results wereobtained.