Consider the Möbius band, and take the middle circle in it (so that it deformation retracts onto it). Glue the upper boundary of a cylinder through it. This gives a space that deformation retracts into the Möbius band and into the cylinder. How can one show this doesn't embed into $\Bbb R^3$?
2026-03-25 23:39:17.1774481957
A space that deformation retracts into the cylinder and Möbius band doesn't embed in $\Bbb R^3$.
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