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تسجيل مستخدم جديدTop-nilpotent enveloping semigroups and pro-nilsystems
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In this paper, it is shown that for $dinmathbb{N}$, a minimal system $(X,T)$ is a $d$-step pro-nilsystem if its enveloping semigroup is a $d$-step top-nilpotent group, answering an open question by Donoso. Thus, combining the previous result of Donoso, it turns out that a minimal system $(X,T)$ is a $d$-step pro-nilsystem if and only if its enveloping semigroup is a $d$-step top-nilpotent group.
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We prove that the maximal infinite step pro-nilfactor $X_infty$ of a minimal dynamical system $(X,T)$ is the topological characteristic factor in a certain sense. Namely, we show that by an almost one to one modification of $pi:X rightarrow X_infty$,
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The regionally proximal relation of order $d$ along arithmetic progressions, namely ${bf AP}^{[d]}$ for $din N$, is introduced and investigated. It turns out that if $(X,T)$ is a topological dynamical system with ${bf AP}^{[d]}=Delta$, then each ergo
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