I am currently working on a problem for which this knowledge could greatly reduce the number of cases, but I have yet to find anything after searching online. Are the closed unbounded subsets of $\mathbb{R}$ known up to homeomorphism?


References would be greatly appreciated.



Are the closed and unbounded subsets of $\mathbb{R}$ known up to homeomorphism?
Infinite, complete, separable linear order with at most countably many jumps and not both a greatest and least element.


See 
<http://www.math.uni-hamburg.de/home/geschke/papers/SeparableLinearOrders2.pdf>


