Klein-bottle meaning

klīn
A one-sided topological surface having no inside or outside. It is depicted in ordinary space by inserting the small open end of a tapered tube through the side of the tube and making it contiguous with the larger open end, although a true Klein bottle would not intersect itself.
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A smooth surface that has no inside or outside. It is often pictured in ordinary space as a tube that bends back upon itself, entering through the side and joining with the open end. A true Klein bottle, which cannot be constructed in ordinary three-dimensional space, would not actually intersect itself. The Klein bottle is named after the German mathematician Felix Klein (1849–1925).
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(mathematics) The closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.
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Origin of klein-bottle

  • After Felix Klein (1849–1925), German mathematician

    From American Heritage Dictionary of the English Language, 5th Edition

  • Named after German mathematician Felix Klein (1849-1925) who first described such a surface in 1882. Bottle seems to have come from a misreading or mistranslation of German Fläche (“surface") as Flasche (“bottle").

    From Wiktionary