Are non-orientable manifolds necessarily compact?












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If not, what is an example of a non-compact, open manifold that is non-orientable? So if non-orientability $Rightarrow$ compactness, is there a theorem and what is the proof?










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    If not, what is an example of a non-compact, open manifold that is non-orientable? So if non-orientability $Rightarrow$ compactness, is there a theorem and what is the proof?










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      -1












      -1








      -1







      If not, what is an example of a non-compact, open manifold that is non-orientable? So if non-orientability $Rightarrow$ compactness, is there a theorem and what is the proof?










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      If not, what is an example of a non-compact, open manifold that is non-orientable? So if non-orientability $Rightarrow$ compactness, is there a theorem and what is the proof?







      general-topology compactness compact-manifolds non-orientable-surfaces






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      asked Nov 26 at 2:24









      Mr X

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          A Möbius strip without boundary is not compact.






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          • True. I think was also asking for, assuming one exists, is an example of a non-orientable manifold that is not totally bounded.
            – Mr X
            Nov 26 at 18:26










          • @MrX: I'm not sure what that means for a general topological manifold. How about gluing an infinitely long boundaryless ribbon to your Möbius strip at right angles?
            – Henning Makholm
            Nov 26 at 18:33













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          1 Answer
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          1 Answer
          1






          active

          oldest

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          active

          oldest

          votes






          active

          oldest

          votes









          5














          A Möbius strip without boundary is not compact.






          share|cite|improve this answer





















          • True. I think was also asking for, assuming one exists, is an example of a non-orientable manifold that is not totally bounded.
            – Mr X
            Nov 26 at 18:26










          • @MrX: I'm not sure what that means for a general topological manifold. How about gluing an infinitely long boundaryless ribbon to your Möbius strip at right angles?
            – Henning Makholm
            Nov 26 at 18:33


















          5














          A Möbius strip without boundary is not compact.






          share|cite|improve this answer





















          • True. I think was also asking for, assuming one exists, is an example of a non-orientable manifold that is not totally bounded.
            – Mr X
            Nov 26 at 18:26










          • @MrX: I'm not sure what that means for a general topological manifold. How about gluing an infinitely long boundaryless ribbon to your Möbius strip at right angles?
            – Henning Makholm
            Nov 26 at 18:33
















          5












          5








          5






          A Möbius strip without boundary is not compact.






          share|cite|improve this answer












          A Möbius strip without boundary is not compact.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Nov 26 at 2:27









          Henning Makholm

          237k16301536




          237k16301536












          • True. I think was also asking for, assuming one exists, is an example of a non-orientable manifold that is not totally bounded.
            – Mr X
            Nov 26 at 18:26










          • @MrX: I'm not sure what that means for a general topological manifold. How about gluing an infinitely long boundaryless ribbon to your Möbius strip at right angles?
            – Henning Makholm
            Nov 26 at 18:33




















          • True. I think was also asking for, assuming one exists, is an example of a non-orientable manifold that is not totally bounded.
            – Mr X
            Nov 26 at 18:26










          • @MrX: I'm not sure what that means for a general topological manifold. How about gluing an infinitely long boundaryless ribbon to your Möbius strip at right angles?
            – Henning Makholm
            Nov 26 at 18:33


















          True. I think was also asking for, assuming one exists, is an example of a non-orientable manifold that is not totally bounded.
          – Mr X
          Nov 26 at 18:26




          True. I think was also asking for, assuming one exists, is an example of a non-orientable manifold that is not totally bounded.
          – Mr X
          Nov 26 at 18:26












          @MrX: I'm not sure what that means for a general topological manifold. How about gluing an infinitely long boundaryless ribbon to your Möbius strip at right angles?
          – Henning Makholm
          Nov 26 at 18:33






          @MrX: I'm not sure what that means for a general topological manifold. How about gluing an infinitely long boundaryless ribbon to your Möbius strip at right angles?
          – Henning Makholm
          Nov 26 at 18:33




















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