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If each $t\\in T$ is onto, $(\\pi,T,X)$ is called surjective; and if each $t\\in T$ is 1-1 onto $(\\pi,T,X)$ is called invertible and in latter case it induces $\\pi^{-1}\\colon X\\times T\\rightarrow X$ by $(x,t)\\mapsto xt:=t^{-1}x$, denoted $(\\pi^{-1},X,T)$. In this paper, we show that $(\\pi,T,X)$ is equicontinuous surjective iff it is uniformly distal iff $(\\pi^{-1},X,T)$ is equicontinuous surjective. 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