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Apr 21, 2011 at 14:52 comment added Mark Grant 1. I think I misunderstood the real question - if this was whether a map which induces equivalences of all fibre bundles is a homotopy equivalence, then Oscar seems to have come up with a good answer! 2. I wish MO had been around when I was your age :)
Apr 21, 2011 at 1:52 comment added Honglu Thanks very much! I start to figure out why all of these answers work. Since all of the answers are of great help, I'm quite uncertain whose answer to accept, though it's merely formal.
Apr 20, 2011 at 13:21 history answered Mark Grant CC BY-SA 3.0