2208.14253
SPLIT SQUARE AND SPLIT CARPET AS EXAMPLES OF NON-METRIZABLE IFS ATTRACTORS
Krzysztof Leśniak, Magdalena Nowak
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: (i) Q is a strict attractor for the 1/2-IFS by reducing to the split interval and invoking a product-IFS lemma; (ii) the split carpet SC is a strict attractor with full basin for the 3-adic IFS omitting the center. The candidate solution proves the same results directly via Vietoris subbasis checks (V− hitting using subrectangles/cells and V+ via triviality for Q and a nested-compact argument for SC). Both arguments are logically sound; they differ in technique.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The work contributes clear, well-motivated examples of non-metrizable strict attractors within IFS theory. Proofs are correct and concise, and the exposition is generally clear. Minor additions could further aid readers unfamiliar with hyperspace convergence and with the mechanics of the stage-set inductions.