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• From wikipedia

In mathematics, the Klein bottleis an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. More formally, the Klein bottle is a two-dimensional manifold on which one cannot define a normal vector at each point that varies continuously over the whole manifold. Other related non-orientable surfaces include the Möbius strip and the real projective plane. While a Möbius strip is a surface with a boundary, a Klein bottle has no boundary. For comparison, a sphere is an orientable surface with no boundary.

This is actually not a real Klein bottle. Scientists believe that in the current three-dimensional world, this kind of bottle cannot be filled. Only in the four-dimensional world can the Klein bottle be filled. According to analysis, the real Klein bottle is not directly connected to the bottom, but the bottleneck passes through the four-dimensional space and then connects to the bottom of the bottle, so there is no distinction between inside and outside.

在数学领域中，克莱因瓶（德语：Kleinsche Flasche）是指一种无定向性的平面，比如二维平面，就没有“内部”和“外部”之分。克莱因瓶最初的概念提出是由德国数学家费利克斯·克莱因提出的。克莱因瓶和莫比乌斯带非常相像。

这实际上不是真正的克莱因瓶。真正的克莱因瓶，科学家认为在目前的三维世界中，这种瓶子是不可能被装满的，只有在四维世界中克莱因瓶才能被装满，据分析，真正的克莱因瓶并不是直接和底部相连的，而是瓶颈穿过了四维空间后再和瓶底相连，因此没有内外之分。