Vol. 72, No. 1, 1977

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Approximate fibrations and a movability condition for maps

Donald S. Coram and Paul Frazier Duvall, Jr.

Vol. 72 (1977), No. 1, 41–56

In a previous paper the authors defined the approximate homotopy lifting property and studied its implications. This property is a generalization of the homotopy lifting property of classical fiber space theory. Here a necessary and sufficient condition on point-inverses for a map to have the approximate homotopy lifting property for n-cells is given; and the approximate homotopy lifting property for n-cells is shown to imply the approximate homotopy lifting property for all spaces. A corollary is that, in a fairly general context, any two point-inverses of a Serre (weak) fibration have the same shape. By combining these results with results of L. Husch, some conditions are obtained under which a map between manifolds can be approximated by locally trivial fibrations.

Mathematical Subject Classification
Primary: 55F65, 55F65
Received: 3 May 1976
Published: 1 September 1977
Donald S. Coram
Paul Frazier Duvall, Jr.