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Please see this image

I think that image's surface is like Möbius. So not homeomorphic to sphere. How can I judge and explain about that in usual topology $\mathbb{R}^3$?

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    $\begingroup$ Looks like an orientable surface of genus $2$ to me. $\endgroup$ – Angina Seng Oct 11 '19 at 0:37
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    $\begingroup$ It's important not to get confused with how a surface is embedded iin R^3 and its homeomorphism type. $\endgroup$ – Andres Mejia Oct 11 '19 at 4:09
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If you cut along the marked green curve, reposition the surface some, and then reglue, you can see that it is exactly a genus two surface.

enter image description here

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    $\begingroup$ nice pictures! :) $\endgroup$ – Andres Mejia Oct 11 '19 at 4:07
  • $\begingroup$ Thank you for your answer and picture. :) $\endgroup$ – rgdadl Oct 11 '19 at 5:45

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