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Let M be an (n – 1) -dimensional manifold in Rn. Let M (Є) be the set of end-points of normal vectors (in both directions) of length Є and suppose Є is small enough so that M(Є) is also an (n- 1)-dimensional manifold. Show that M(Є) is orientable (even if M is not). What is M(Є ) if M is the M"{o}bius strip? |
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