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Klein bottle, a closed one-sided surface, the concept for which was introduced by F. Klein in 1874.
A Klein surface can be made from a tube that is open at both ends by bending the tube, passing its narrower end through the
wall, and “identifying” the two end circles (see Figure 1,a). A surface is obtained that has a self-intersecting line (see Figure l,b). A Klein surface without self-intersection can only be realized in four-dimensional space.