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Abstract
In this thesis we study approximate fibrations p : E (--->) B between separable metric spaces which can be regarded as a generalization of Hurewicz fiberings.
Under an additional condition on the approximate path lifting functions of the map p, we obtain the following results. The approximate fibration p becomes a strongly regular map, and hence it is a Hurewicz fibration if the fibers are ANR's, and it is locally trivial in the case when the fibers are Q-manifolds.
If we further assume the base space B and the fibers of p are ANR's, then the total space E is an ANR provided, either there exists a finite dimensional (epsilon)-retract of B, for each (epsilon) < 0, or the space E is a countable union of finite dimensional compact spaces.
In the case when the fibers are non-compact, by using the notion of fiberwise one-point compactification we obtained similar results.
