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Approximating Approximate Fibrations by Fibrations

Published online by Cambridge University Press:  20 November 2018

L. S. Husch
L. S. Husch*
Affiliation:
University of Tennessee, Knoxville, Tennessee 37916
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A map p: E → B between metric spaces has the approximate homotopy lifting property with respect to the space X if given a cover Ū of B and maps g: X → E and H: X × [0, 1] → B such that H(x, 0) = pg(x) for all x ϵ X, then there exists a map G: X × [0, 1] → E such that G(x, 0) = g(x) and pGt and Ht are Ū-close for all x ϵ X and t ϵ [0, 1]; i.e. given (x, t) ∊ X × [0, 1], there exists U × Ū such that pG(x, t) and H(x, t) are elements of U.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 897 - 913
Copyright
Copyright © Canadian Mathematical Society 1977

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