Now I know that the fibers of a fibration are homotopy equivalent, but I was wondering if the converse was true if we have the stronger conidition that the fibers are homeomorphic. If a map whose fibers are homeomorphic do we have a fibration, and if we weaken it to just homotopy equivalent are there additional conditions we can give so that the map is a fibration.
Map whose fibers are homotopic/homeomorphic are is a fibration
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fiber-bundles
fibration
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0Suppose that X and Y are two topological spaces with the *same* underlying set, and such that the identity function $X\to Y$ is continuous. All fibers are homotopy equivalent, and in fact homeomorphic. Is it a fibration? – 2017-02-19
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0No, not neccesarily. Thanks. – 2017-02-19
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0Why did you delete the question?! It is certainly a useful question to have around. – 2017-02-19
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0I just wasn't sure if this was a good enough question for the site is all. I have undeleted. – 2017-02-20