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In studying quasifibration I have a question.

When a quasifibration $F\to E\to B$ is a Hurewicz fibration?

If $F,E$ and $B$ are CW-complex, it is right?

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Having CW complexes is certainly not enough. A "classical" example of a quasifibration that is not a Hurewicz fibration is the projection of an L-shape onto an interval, so that the fiber over one endpoint is an interval and the fiber over all other points is a point. All of these spaces are CW-complexes. –  Mike Shulman Apr 6 '11 at 3:40
@Mike: you've provided a valid answer. Why don't you post it as one? –  John Klein Apr 6 '11 at 11:51

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