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Übersetzungen für „Klein“ im Englisch » Deutsch-Wörterbuch (Springe zu Deutsch » Englisch)

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For example, the Klein bottle has no "boundary", where the surface stops abruptly, and it is non-orientable, as reflected in the one-sidedness of the immersion.
en.wikipedia.org
This is an immersion of the Klein bottle in three dimensions.
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Gluing the circles together will produce a new, closed manifold without boundary, the Klein bottle.
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He makes the same restriction on geometrically atoroidal manifolds (which he calls topologically atoroidal) and in addition requires them to avoid incompressible boundary-parallel embedded Klein bottles.
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The Klein bottle, proper, does not self-intersect.
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Note that this is an abstract gluing in the sense that trying to realize this in three dimensions results in a self-intersecting Klein bottle.
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Gluing two projective planes creates the Klein bottle.
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This immersion is useful for visualizing many properties of the Klein bottle.
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Other examples of closed manifolds are the torus and the Klein bottle.
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Note that in three-dimensional space, a Klein bottle's surface must pass through itself.
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