Corrigendum to "Syndetically proximal pairs" [J. Math. Anal. Appl. 379 (2011) 656--663]

TL;DR

This paper corrects a previous theorem on syndetically proximal pairs by providing a counterexample and establishing conditions under which the original conclusion is valid.

Contribution

It presents a counterexample to a prior theorem and offers sufficient conditions for its validity, refining the understanding of syndetically proximal pairs.

Findings

Counterexample to Theorem 9 in the original paper

Sufficient conditions for the theorem's conclusion to hold

Clarification of the theorem's applicability

Abstract

We give a counterexample to Theorem 9 in [T.K. Subrahmonian Moothathu, Syndetically proximal pairs, J. Math. Anal. Appl. 379 (2011) 656--663]. We also provide sufficient conditions for the conclusion of Theorem 9 to hold.