Non-orientable manifold

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A manifold that does not admit an orientation. Such are, for example, the Möbius strip, the Klein surface and the projective spaces $\mathbf{RP}^n$ of even dimension.

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Non-orientable manifold. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article