2203.01423
Minimal sets on continua with a dense free interval
Michaela Mihoková
correcthigh confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem A and its case-by-case proofs are coherent and justified via a dimension-based retraction lemma and a clean permutation-of-components argument. The candidate solution reproduces the statements but repeatedly relies on a false general claim that any locally connected subcontinuum of a compact metric space is a retract, omitting the paper’s essential hypothesis dim(X\Y) ≤ 1 for such retractions. This gap affects several steps where the model transfers minimal sets between X and subcontinua.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper gives a clear and useful classification of minimal sets on continua with a dense free interval, generalizing and unifying known results for classical spaces (arc, circle, Warsaw circle, topologist’s sine curve). The core tools are standard and used carefully. I recommend minor revisions to improve clarity around when retractions are available (explicitly flagging uses of Lemma 10 vs. AR properties of arcs) and to add a few signposts in the proofs.