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Sep 6, 2013 at 15:35 comment added Niemi Alright. Thanks again for your help.
Sep 6, 2013 at 15:30 comment added James Cranch No. Similar techniques to this one will work quite well in greater generality, but only for the very pleasant kinds of spaces favoured by homotopy theorists.
Sep 6, 2013 at 15:13 history edited James Cranch CC BY-SA 3.0
changing answer to reflect changed emphasis of question
Sep 6, 2013 at 15:13 comment added Niemi Thanks a lot for the answer. Do you know a characterization of the cases where the statement is true?
Sep 6, 2013 at 15:00 history answered James Cranch CC BY-SA 3.0