Can someone give me a hint on proving that the fibre of a fibration $f: Y \to X$ is homotopy equivalent to its homotopy fibre $Y \times_X X^I$?
fibre of a fibration is homotopy equivalent to its homotopy fibre
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general-topology
homotopy-theory
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1Not a hint, but a couple of arguments and references can be found [in this MO-thread](http://mathoverflow.net/questions/53729/the-fiber-of-a-serre-fibration). – 2011-05-10
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0Thanks, I already found this. But I don't want the complete argument. – 2011-05-10
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0The first step would be to construct a continuous function from one to the other. There appears to be a good choice *from* the fibre *to* the homotopy fibre. – 2011-05-10