  A quasi-continuous dynamical system is a pair $(X,f)$ consisting of a
topological space $X$ and a mapping $f: X\to X$ such that $f^n$ is
quasi-continuous for all $n \in \mathbb N$, where $\mathbb N$ is the set of
non-negative integers. In this paper, we show that under appropriate
assumptions, various definitions of the concept of topological transitivity are
equivalent in a quasi-continuous dynamical system. Our main results establish
the equivalence of topological and point transitivity in a quasi-continuous
dynamical system. These extend some classical results on continuous dynamical
systems in [3], [10] and [25], and some results on quasi-continuous dynamical
systems in [7] and [8].
