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In the notes available here, the first example (p. 2) says that the Mobius band is non-orientable because there is an obstruction to a map sending a disk to the band. I don't really understand what's going on here; I've never heard orientablility characterized in terms of attaching disks and I'm pretty sure you can attach a disk to the Mobius strip. I really need to understand this example and any help would be appreciated.

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