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In this work , we study different chaotic properties of the product space on a onestep shift of a finite type, as well as other spaces. We prove that the product is Lyapunove ε –unstable if and only if at least one or is Lyapunove ε – unstable. Also, we show that and locally everywhere onto (l.e.o) if and only if is locally everywhere onto (l.e.o) .

Some Chaotic Results of Product on Zero Dimension Spaces