关于全不连通的广义Sierpinski地毯
On totally disconnected generalised Sierpinski carpets
摘要：
广义Sierpinski地毯是一种平面集合，它是对著名的Sierpinski地毯的推广，并通过图案序列来定义。我们研究了广义地毯构造中第k次迭代时的集合结构，k大于或等于1。随后，我们表明，某些家庭的模式提供总断开由此产生的广义地毯。此外，类似的结果甚至在更一般的情况下也成立。最后，我们应用所得到的结果，以给出一个例子的全不连通的广义地毯盒计数维2。
英文摘要：
Generalised Sierpinski carpets are planar sets that generalise the well-known Sierpinski carpet and are defined by means of sequences of patterns. We study the structure of the sets at the kth iteration in the construction of the generalised carpet, for k greater than or equal to 1. Subsequently, we show that certain families of patterns provide total disconnectedness of the resulting generalised carpets. Moreover, analogous results hold even in a more general setting. Finally, we apply the obtained results in order to give an example of a totally disconnected generalised carpet with box-counting dimension 2.
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