Transitivity and sensitivity of semigroup actions on uniform spaces

In this paper, we investigate several forms of transitivity and sensitivity in the dynamical system of semigroup actions. Firstly, we derive some equivalent conditions for a dynamical system to be sensitive. In particular, it is proved that an M-system with an equicontinuous point is minimal as well as equicontinuous, every syndetically transitive system with equicontinuous point is minimal as well as equicontinuous. Also, we derive equivalent conditions for a system to be almost equicontinuous in terms of sensitivity and equicontinuity. Besides, some results on point transitive and densely point transitive system on uniform spaces are obtained.