Quartic plane curve

In mathematics, a solid Klein bottle is a 3-manifold (with boundary) homeomorphic to the quotient space obtained by gluing the top of $\scriptstyle D^{2}\times I$ (cylinder) to the bottom by a reflection, i.e. the point $\scriptstyle (x,0)\,$ is identified with $\scriptstyle (r(x),1)\,$ where $\scriptstyle r\,$ is reflection of the disc $\scriptstyle D^{2}\,$ across a diameter.

Mö x I: the circle of black points marks an absolute deformation retract of this space, and any regular neighbourhood of it has again boundary as a Klein bottle, so Mö x I is an onion of Klein bottles

Note the boundary of the solid Klein bottle is a Klein bottle.

Alternatively, one can visualize the solid Klein bottle as the trivial product $\scriptstyle M{\ddot {o}}\times I$, of the möbius strip and an interval $\scriptstyle I=[0,1]$. 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: $\scriptstyle M{\ddot {o}}\times [{\frac {1}{2}}-\varepsilon ,{\frac {1}{2}}+\varepsilon ]$ and whose boundary is a Klein bottle as previously noticed

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