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For no appreciatable reason I've been trying to figure out 2-manifolds. Unfortunately, I've been struggling to find good enough sources on learning the basics, so it's pretty likely that my question will betray my lack of understanding of the basic topological concepts, which I believe to be a good thing.

Imagine we cut a circural hole in a sphere. It will have a single boundary. Let's also take a Möbius strip. It also has a single boundary. let's glue those boundaries together. What will be the resulting shape? What it will be homeomorphic to? It might be a cliché thing to say in the field, but I have hard times imagining the resulting object.

Might be a duplicate with Gluing a Möbius strip into a sphere. - I do not understand either the question nor an answer.

Okay, after getting some answers that cleared things up for me, and re-reading & re-analyzing the question above, I can confirm that indeed I posted a duplicate question. I'm sorry. :(

VienLa
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    The resulting space is the two dimensional real projective space. You can explicitly write down the homeomorphism. – ThorbenK May 26 '19 at 17:06
  • Can you please make the question body with no unnecessary information... –  May 26 '19 at 17:06
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    A source: https://en.wikipedia.org/wiki/Real_projective_plane – Greg Martin May 26 '19 at 17:07
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    A sphere with a circular hole is a disc. Gluing a disc to the boundary of a Möbius strip results in the real projective plane. – user10354138 May 26 '19 at 17:07
  • Thanks for providing an answer. It now makes perfect sense. If you post it as an answer I will mark it as accepted. – VienLa May 26 '19 at 17:24

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