Vol. 30, No. 2, 1969

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Conditions for a mapping to have the slicing structure property

Gerald S. Ungar

Vol. 30 (1969), No. 2, 549–553

Let p : E B be a fibering in the sense of Serre. As is well known the fibering need not be a fibering in any stronger sense. However it is expected that if certain conditions are placed on E,p or B then p might be a fibration in a stronger sense. This paper gives such conditions.

The main result of this paper is:

Theorem 1. Let p be an n-regular perfect map from a complete metric space (E,d) onto a locally equiconnected space B. If dimE ×B n then p has the slicing structure property (in particular p is a Hurewicz fibration).

The following definitions will be needed.

Mathematical Subject Classification
Primary: 55.50
Received: 30 October 1968
Published: 1 August 1969
Gerald S. Ungar