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Solid Klein bottle : ウィキペディア英語版
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 \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 \scriptstyle M\ddot\times I, of the möbius strip and an interval \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: \scriptstyle M\ddot\times() and whose boundary is a Klein bottle.
==References==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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