A shape fibration with fibers of different shape

James Edgar Keesling and Sibe Mardesic

Vol. 84 (1979), No. 2, 319–331

DOI: 10.2140/pjm.1979.84.319

Abstract

Let E and B be metric continua. Let p : E → B be a shape fibration in the sense of Mardešić and Rushing. If B is arcwise connected, then all the fibers of p have the same shape. This is also true if B is connected by shape paths in the sense of Krasinkiewicz and Minc. It had been asked whether that this would be true without any assumptions other than B being a continuum. In this paper an example is given of a shape fibration p : E → B with E and B metric continua such that p has fibers of different shape.

Mathematical Subject Classification 2000

Primary: 55R65

Secondary: 55P55

Milestones

Received: 3 October 1978

Revised: 17 January 1979

Published: 1 October 1979