Erratum to “A note on uniform convergence and transitivity” [Chaos, Solitons and Fractals 45 (2012) 759–764]

Let (fn)(fn) be a given sequence of continuous selfmaps of a compact metric space X which converges uniformly to a continuous selfmap f of the compact metric space X. In this note, we present a counterexample which shows that Theorems 3.9–3.11 obtained by us in [Chaos, Solitons and Fractals 45 (2012) 759–764] are not true and give the correct proofs of Theorems 3.4–3.7 in [Chaos, Solitons and Fractals 45 (2012) 759–764]. We also obtain a equivalence condition for the uniform map f to be syndetically sensitive or cofinitely sensitive or multi-sensitive or ergodically sensitive and a sufficient condition the uniform map f to be totally transitive or topologically weak mixing.