Definitions

from The American Heritage® Dictionary of the English Language, 5th Edition.

  • noun 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.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • noun mathematics The closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • noun a closed surface with only one side; formed by passing one end of a tube through the side of the tube and joining it with the other end

Etymologies

from The American Heritage® Dictionary of the English Language, 4th Edition

[After Felix Klein, (1849–1925), German mathematician.]

from Wiktionary, Creative Commons Attribution/Share-Alike License

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").

Examples

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