Coarse non-wandering sets and their filtration

The paper’s statements (Theorem A and Theorem B) and their proofs are correct. The candidate solution establishes the same results. It proves Part A (filtration, union equals X, and Ω(f)=Ω0(f)) in line with Proposition 3.6 and Lemma 3.4, and Part B (equivalence of (1)–(3)) via a direct proof of (1)⇒(3) that differs from, but is compatible with, the paper’s route ((1)⇒(2) via Lemma 4.3, then (2)⇔(3) by definition). A minor definitional subtlety: the paper defines Ω−ε(f) using the rider x∈Ω0(f), whereas the candidate introduces Ω−ε(f) first without explicitly stating that rider and then notes the convention; this does not affect the equivalences proved.