A shape fibration with fibers of different shape

Abstract

Let E and B be metric continua. Let p:E~>B be a shape fibration in the sense of Mardesic 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 Mine. 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.