Conditions for a mapping to have the slicing structure property

Gerald S. Ungar

Vol. 30 (1969), No. 2, 549–553

DOI: 10.2140/pjm.1969.30.549

Abstract

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

Milestones

Received: 30 October 1968

Published: 1 August 1969