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Abstract/Details
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.
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
ON APPROXIMATE FIBRATIONS
Source
DAI-B 42/03, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
University/institution
University of Connecticut
University location
United States -- Connecticut
Source type
Dissertation or Thesis
Document type
Dissertation/Thesis
Dissertation/thesis number
8117603
ProQuest document ID
303124410
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303124410/abstract