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In the proof of theorem 2B.1 page 169-170 of Hatcher (generalized Jordan curve theorem), item (b) is proved by induction on k and the case k=0 is handled by noticing that S^n - h(S^0) is homeomorphic to S^(n-1) xR. How does he know that [tex]\widetilde{H}_i(\mathbb{S}^{n-1} \times \mathbb{R})[/tex] isZif i=n-1 and 0 otherwise?

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# Homology of S^n x R

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