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In mathematics, a solid Klein bottle is a three-dimensional topological space whose boundary is the Klein bottle.
It is homeomorphic to the quotient space obtained by gluing the top disk of a cylinder D 2 × I {\displaystyle \scriptstyle D^{2}\times I} to the bottom disk by a reflection across a diameter of the disk.
Alternatively, one can visualize the solid Klein bottle as the trivial product M o ¨ × I {\displaystyle \scriptstyle M{\ddot {o}}\times I} , of the möbius strip and an interval I = {\displaystyle \scriptstyle I=}. In this model one can see that the core central curve at 1/2 has a regular neighborhood which is again a trivial cartesian product: M o ¨ × {\displaystyle \scriptstyle M{\ddot {o}}\times } and whose boundary is a Klein bottle.