2111.01927
Porosities of the sets of attractors
Pawe l Klinga, Adam Kwela
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves Theorem 4.1 (A[0,1] is not σ-strongly porous in K[0,1]) via a careful coding of Cantor-like attractors by sequences in [-3/2, 3/2]^N and a Baire-category argument in the sequence space, with detailed local 0.99-robustness estimates around a chosen attractor, which is correct and complete. The candidate solution reaches the same conclusion but relies on a false auxiliary lemma: it asserts that strong porosity is hereditary to subspaces. This is not true in general metric spaces (and is unnecessary here). While the argument can be repaired by using the true facts that strongly porous implies nowhere dense and that nowhere denseness is hereditary to subspaces (as noted in the paper’s porosity discussion), the proof as written is flawed.
Referee report (LaTeX)
\textbf{Recommendation:} reject
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper’s main theorem is proved with a robust and carefully detailed argument using coding and Baire category in a complete product space, and is correct. The model’s proof, while elegant in spirit, relies on an incorrect lemma (that strong porosity is hereditary to subspaces), so it is not correct as written; however, the core idea can be repaired by replacing that step with the hereditary property of nowhere denseness.