Re: Homology, irrational foliation of the torus

James wrote:
If I take the irrational foliation of the torus, that is, the image of a line with irrational slope under the covering map R^2 ----> Torus, and identify the foliation to a point, how can I calculate its homology? I have done it in the case that we take a line with rational slope, but irrational I don't see how to put a CW structure on it.

Does a CW complex have to satisfy any nice separation axiom?
Because the quotient space of the the torus with points
lying on a line of fixed irrational slope isn't even T^0:
even point is dense.
.