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Nov 20, 2011 at 1:55 vote accept Guillaume Brunerie
Nov 19, 2011 at 1:34 answer added Tom Goodwillie timeline score: 5
Nov 19, 2011 at 0:46 comment added Thomas Belulovich The answer is yes whenever $S$ is a CW-complex, or more generally what is called a cofibrant object in the standard model category structure on Top. These consist of cell-complexes (but the cells can be attached in any order), as well as retracts of cell complexes.
Nov 19, 2011 at 0:13 history asked Guillaume Brunerie CC BY-SA 3.0