We deal with the question of Masayoshi Hata: is every Peano continuum a topological fractal? A compact space X is a topological fractal if there exists $\mathcal{F}$ a finite family of self-maps on X such that $X={\bigcup }_{f\in \mathcal{F}}f(X)$ and for every open cover $\mathcal{U}$ of X there is $n\in \mathbb{N}$ such that for all maps $f_1,\dots ,f_n\in \mathcal{F}$ the set $f_1\circ \dots \circ f_n(X)$ is contained in some set $U\in \mathcal{U}$.

In the paper we present some idea how to extend a topological fractal and we show that a Peano continuum is a topological fractal if it contains so-called self regenerating fractal with nonempty interior. A Hausdorff topological space A is a self regenerating fractal if for every non-empty open subset U, A is a topological fractal for some family of maps constant on $A\setminus U$.

The notion of self regenerating fractal much better reflects the intuitive perception of self-similarity. We present some classical fractals which are self regenerating.

我们处理 Masayoshi Hata 的问题：每个 Peano 连续统都是一个拓扑分形吗？一个紧空间X是一个拓扑分形，如果存在$\mathcal{F}$X上的有限自映射族，使得$X={\bigcup }_{F\in \mathcal{F}}F(X)$ 并且对于每个打开的盖子 $\mathcal{你}$的X有$n\in \mathbb{N}$ 这样对于所有地图 $F_1,\dots ,F_n\in \mathcal{F}$ 集合 $F_1\circ \dots \circ F_n(X)$ 包含在某个集合中 $你\in \mathcal{你}$.

在论文中，我们提出了如何扩展拓扑分形的一些想法，并且我们证明了皮亚诺连续统如果包含所谓的内部非空的自再生分形，则它是拓扑分形。豪斯多夫拓扑空间A是一个自再生分形，如果对于每个非空开放子集U，A是某个映射族的拓扑分形$\mathrm{一种}\setminus 你$.

自再生分形的概念更好地反映了对自相似性的直观感知。我们提出了一些自我再生的经典分形。