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Hempel, in his 1987 article "Residual Finiteness for 3-Manifolds", shows that if 𝑀$M$ is a compact Haken 3-manifold, then 𝜋1(𝑀)$\pi_1(M)$ is residually finite. In the proof he starts by reducing the case to '𝑀'$M$ is closed and irreducible'. Why can he so easily do that?

Thanks in advance!

Hempel, in his 1987 article "Residual Finiteness for 3-Manifolds", shows that if 𝑀 is a compact Haken 3-manifold, then 𝜋1(𝑀) is residually finite. In the proof he starts by reducing the case to '𝑀 is closed and irreducible'. Why can he so easily do that?

Thanks in advance!

Hempel, in his 1987 article "Residual Finiteness for 3-Manifolds", shows that if $M$ is a compact Haken 3-manifold, then $\pi_1(M)$ is residually finite. In the proof he starts by reducing the case to '$M$ is closed and irreducible'. Why can he so easily do that?

Thanks in advance!

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Residual Finiteness for 3-Manifolds Hempel

Hempel, in his 1987 article "Residual Finiteness for 3-Manifolds", shows that if 𝑀 is a compact Haken 3-manifold, then 𝜋1(𝑀) is residually finite. In the proof he starts by reducing the case to '𝑀 is closed and irreducible'. Why can he so easily do that?

Thanks in advance!