
The \h{Sierpinski Triangle} is obtained as the residual set
remaining when one begins with a triangle and applies the
operation of dividing it  into four equal triangles and
omitting the interior of the center one, then repeats this
operation on each of the surviving 3 triangles, then repeats
again on the surviving 9  triangles, and so on $\cdots$ .
See \cite[Example 2.7]{cd1994}.

The Sierpinski Triangle is homeomorphic to the unique
nonempty compact set $K$ of the complex plane that satisfies
$$
 K= w_1(K) \cup  w_2(K) \cup w_3(K) \quad ,
$$
where $w_1$, $w_2$, $w_3$
are maps of the complex plane defined by
$w_1(z)=z/2$, $w_2=(z + 1)/2$ and $w_3=(z+i)/2$.
