In this paper, it is shown that if a dynamical system is null and distal, then it is equicontinuous. It turns out that a null system with closed proximal relation is mean equicontinuous. As a direct application, it follows that a null dynamical system with dense minimal points is also mean equicontinuous. Meanwhile, a distal system with trivial $text{Ind}_{fip}$-pairs, and a non-trivial regionally proximal relation of order $infty$ is constructed.
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