Yeah that should work I think. Maybe more interesting would be whether there exists an example which is not locally homeomorphic to IR (I think you're example still fulfills that). But I believe that is solved by using something like the long line and looking at e.g. ω~0~\times 0. Is there an example that is nowhere locally homeomorphic to IR?
Yeah that should work I think. Maybe more interesting would be whether there exists an example which is not locally homeomorphic to IR (I think you're example still fulfills that). But I believe that is solved by using something like the long line and looking at e.g. ω~0~\times 0. Is there an example that is nowhere locally homeomorphic to IR?