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?
general-topology compactness compact-manifolds non-orientable-surfaces
asked Nov 26 at 2:24
Mr X
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up vote
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down vote
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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
asked Nov 26 at 2:24
Mr X
19311
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
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
asked Nov 26 at 2:24
Mr X
19311
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
general-topology compactness compact-manifolds non-orientable-surfaces
asked Nov 26 at 2:24
Mr X
19311
asked Nov 26 at 2:24
Mr X
19311
asked Nov 26 at 2:24
Mr X
19311
asked Nov 26 at 2:24
Mr X
19311
asked Nov 26 at 2:24
Mr X
19311
19311
add a comment |
add a comment |
1 Answer
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votes
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5
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A Möbius strip without boundary is not compact.
answered Nov 26 at 2:27
Henning Makholm
236k16300534
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
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
A Möbius strip without boundary is not compact.
answered Nov 26 at 2:27
Henning Makholm
236k16300534
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
add a comment |
up vote
5
down vote
A Möbius strip without boundary is not compact.
answered Nov 26 at 2:27
Henning Makholm
236k16300534
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
add a comment |
up vote
5
down vote
up vote
5
down vote
A Möbius strip without boundary is not compact.
answered Nov 26 at 2:27
Henning Makholm
236k16300534
A Möbius strip without boundary is not compact.
answered Nov 26 at 2:27
Henning Makholm
236k16300534
answered Nov 26 at 2:27
Henning Makholm
236k16300534
answered Nov 26 at 2:27
Henning Makholm
236k16300534
answered Nov 26 at 2:27
Henning Makholm
236k16300534
236k16300534
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
add a comment |
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
add a comment |
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