Strongly regular mappings with compact ANR fibers are Hurewicz fiberings

Steve Ferry

Vol. 75 (1978), No. 2, 373–382

DOI: 10.2140/pjm.1978.75.373

Abstract

We prove that a strongly regular map f : E → B with compact separable ANR fibers and complete separable finite dimensional base space B is a Hurewicz fibering. We also show that if f is a Hurewicz fiber map with locally compact ANR fibers and base, then the total space E is an ANR.

Mathematical Subject Classification 2000

Primary: 55R65

Milestones

Received: 2 April 1976

Revised: 26 April 1977

Published: 1 April 1978