I-bundle

In mathematics, an I-bundle is a fiber bundle whose fiber is an interval and whose base is a manifold. Any kind of interval, open, closed, semi-open, semi-closed, open-bounded, compact, even rays, can be the fiber.

Two simple examples of I-bundles are the annulus and the Möbius band, the only two possible I-bundles over the circle ${\displaystyle \scriptstyle S^{1}}$. The annulus is a trivial or untwisted bundle because it corresponds to the Cartesian product ${\displaystyle \scriptstyle S^{1}\times I}$, and the Möbius band is a non-trivial or twisted bundle. Both bundles are 2-manifolds, but the annulus is an orientable manifold while the Möbius band is a non-orientable manifold.

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