The original approach of Hutchinson to fractals considers the defining equation as a fixed point problem, and then applies the Banach Contraction Principle. To do this, the Blaschke Completeness Theorem is essential. Avoiding Blaschke’s result, this note presents an alternative way to fractals via the Kuratowski noncompactness measure. Moreover, our technique extends the existence part of Hutchinson’s Theorem to condensing maps instead of contractions.

中文翻译：

---

没有Blaschke的Hutchinson：分形的另一种方法

Hutchinson最初的分形方法将定义方程视为不动点问题，然后应用Banach收缩原理。为此，Blaschke完整性定理是必不可少的。为了避免Blaschke的结果，本笔记提出了一种通过Kuratowski非紧实度度量替代分形的方法。而且，我们的技术将Hutchinson定理的存在部分扩展到了压缩地图而不是收缩。