广义Cantor集与Hausdorff维数的非拓朴性质  

EXTENDED CANTOR SETS AND THE NON-TOPOLOGICAL PROPERTY OF HAUSDORFF DIMENSION

作　　者：刘华民[1] 郑世斌[1] 

机构地区：[1]郑州大学系统科学与数学系

出　　处：《郑州大学学报（理学版）》1993年第3期1-4,共4页Journal of Zhengzhou University:Natural Science Edition

摘　　要：本文给出了广义Cantor集P_α的概念,算出了广义Cantor集P_α的Hausdorff维数,并证明了任何两个广义Cantor集都是同胚的,从而说明了分形的Hausdorff维数不具有拓扑不变性质。Abstract At first, this paper gives a cancept of extended cantor sets,then gets Hatlsdoff di-mensisn of the eXtended Cantor sets,and also prove that any two extended cantor scts are homeo-morphic.Furthermore,It explains that fractals Hausdorff dimension does not have topologicaI inuar-icant property.

关 键 词：广义CANTOR集 分形 同胚 HAUSDORFF维数 

分 类 号：O[理学] 177.91