Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.01927 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- This paper is another attempt to measure the difference between the family $A[0,1]$ of attractors for iterated function systems acting on $[0,1]$ and a broader family, the set $A_w[0,1]$ of attractors for weak iterated function systems acting on $[0,1]$. It is known that both $A[0,1]$ and $A_w[0,1]$ are meager subsets of the hyperspace $K([0,1])$ (of all compact subsets of $[0,1]$ equipped in the Hausdorff metric). Actually, $A[0,1]$ is even $σ$-lower porous while the question about $σ$-lower porosity of $A_w[0,1]$ is still open. We prove that $A[0,1]$ is not $σ$-strongly porous in $K([0,1])$. Moreover, we show that $A_w[0,1]\setminus A[0,1]$ is dense in $K([0,1])$.