Solid Klein bottle
In mathematics, a solid Klein bottle is a 3-manifold (with boundary) homeomorphic to the quotient space obtained by gluing the top of (cylinder) to the bottom by a reflection, i.e. the point is identified with where is reflection of the disc across a diameter.
Note the boundary of the solid Klein bottle is a Klein bottle.
Alternatively, one can visualize the solid Klein bottle as the trivial product , of the möbius strip and an interval . 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: and whose boundary is a Klein bottle as previously noticed
|This topology-related article is a stub. You can help Wikipedia by expanding it.|