A Note on Sensitivity in Uniform Spaces

In this paper, the notions of periodic point are compared, and the sensitivity of semigroup actions on Hausdorff uniform spaces is studied. We show that for an action of a semigroup on a compact uniform space, if it is syndetically transitive and not minimal, then it is syndetically sensitive. We point out that if an action of a semigroup on a uniform space (does not need to be compact) is topologically transitive, not minimal, and has a dense set of s-periodic points, then it is syndetically sensitive. Additionally, we prove that if an action of a monoid on a uniform space (does not need to be compact) is topologically transitive, not minimal, and has a dense set of FM-periodic points, then it is syndetically sensitive.