Solid Klein bottle

In mathematics, a solid Klein bottle is a three-dimensional topological space (a 3-manifold) 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 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 , of the möbius strip and an interval I = [ 0 , 1 ] . 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 ¨ × [ 1 2 − ε , 1 2 + ε ] and whose boundary is a Klein bottle.