Klein bottle

Klein bottle
a one-sided figure consisting of a tapered tube the narrow end of which is bent back, run through the side of the tube, and flared to join the wide end, thereby allowing any two points on the figure to be joined by an unbroken line.
[1940-45; named after F. KLEIN]

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      topological space, named for the German mathematician Felix Klein, obtained by identifying two ends of a cylindrical surface in the direction opposite that is necessary to obtain a torus. The surface is not constructible in three-dimensional Euclidean space but has interesting properties, such as being one-sided, like the Möbius strip (q.v.); being closed, yet having no “inside” like a torus or a sphere; and resulting in two Möbius strips if properly cut in two.

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Universalium. 2010.

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