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Topological and Algebraic Copies of N in N

We show that the only topological and algebraic copies of N∗ to be found in N∗ are the trivial ones, namely k · N∗ for k ∈ N. A similar statement holds for copies of Z∗ in Z∗. As a consequence, we obtain the corollary that N∗ contains no copies of Z∗ whatever.