A simple proof of a theorem of sensitivity

TL;DR

This paper provides a straightforward proof that transitive, non-minimal semigroups with dense minimal points exhibit sensitivity, and extends the result to systems that are almost open.

Contribution

It offers a simple proof of sensitivity in certain semigroups and generalizes the result to almost open systems.

Findings

Transitive, non-minimal semigroups with dense minimal points are sensitive.

Sensitivity is extended to almost open systems.

Provides a simplified proof of a known theorem.

Abstract

We prove that every transitive and non minimal semigroup with dense minimal points is sensitive. When the system is almost open, we obtain a generalization of this result.