"Dynamical system
semi-topological semi-group
isomorphisim of H-systems
monoidal compactification
transitive pointed systems
inclusive transitive pointed systems."
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In this paper, some relations between the flows and the Enveloping Semi-group were studied. It allows to associate some properties on the topological compactification to any pointed flows. These relations enable us to study a number of the properties of the principles of flows corresponding with using algebric properties. Also in this paper proofs to some theorems of these relations are given.