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.
|