Klein bottle

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Klein bottle

[′klīn ‚bäd·əl]
(mathematics)
The nonorientable surface having only one side with no inside or outside; it resembles a bottle pulled into itself.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
We begin by describing a procedure to topologically spin a properly embedded surface F which is incompressible and [partial derivative]-incompressible in a compact 3-manifold M with boundary consisting of tori and Klein bottles. Topological spinning of F is to add an annulus winding around a torus or Klein bottle boundary component to F and compute the isotopy class of the resulting surface keeping its boundary fixed.
Since [??] is 1-efficient, the peripheral tori or Klein bottles are the only normal surfaces with nonnegative Euler characteristic.
Especially spun normal surfaces represent proper essential surfaces using ideal triangulations of 3-manifolds with tori and Klein bottle boundary components.
In [1], it was proved that the interior of a compact orientable 3-manifold M which is irreducible, atoroidal, anannular, with tori and Klein bottle boundary components has a 1-efficient ideal triangulation.
Both the cross-cap and the Klein bottle offer somewhat more complicated examples of nonorientable surfaces.