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On the existence of cut points of connected generalized Sierpinski carpets
- Publication Year :
- 2022
-
Abstract
- In a previous work joint with Dai and Luo, we show that a connected generalized Sierpi\'nski carpet (or shortly a GSC) has cut points if and only if the associated $n$-th Hata graph has a long tail for all $n\geq 2$. In this paper, we extend the above result by showing that it suffices to check a finite number of those graphs to reach a conclusion. This criterion provides a truly "algorithmic" solution to the cut point problem of connected GSCs. We also construct for each $m\geq 1$ a connected GSC with exactly $m$ cut points and demonstrate that when $m\geq 2$, such a GSC must be of the so-called fragile type.<br />Comment: 28 pages, 7 figures
- Subjects :
- Mathematics - General Topology
Primary 28A80, Secondary 54A05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2204.07706
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.54330/afm.127049