For all questions about Möbius bands, Klein bottles, projective planes or surfaces built from these (via surgeries, gluings...), intersection or boundary problems, embeddings...

# Questions tagged [non-orientable-surfaces]

62 questions

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### Klein bottle contains Möbius band

I read the following: "The Klein bottle contains a copy of the Möbius band".
I assume this means that there is a subspace of the Klein bottle that is homeomorphic to the Möbius band. How do we obtain the Möbius band from the fundamental polygon of…

iwriteonbananas

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### Are non-orientable manifolds necessarily compact?

If not, what is an example of a non-compact, open manifold that is non-orientable? So if non-orientability $\Rightarrow$ compactness, is there a theorem and what is the proof?

Mr X

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