自相似曲线与Whitney型临界集

Self-Similar Curves and Whitney Sets

本文讨论一类（包括Ｋｏｃｈ曲线在内的）自相似曲线，证明了其上的简单曲线是Ｗｈｉｔｎｅｙ型临界集，并在微小扰动下仍是简单曲线．

A class of self-similar curves including Koch curve is defined, and the following result is obtained: If a curve of this class is a simple curve, then it is a Whitney set.