Vol. 84, No. 2, 1979

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A shape fibration with fibers of different shape

James Edgar Keesling and Sibe Mardesic

Vol. 84 (1979), No. 2, 319–331

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
Received: 3 October 1978
Revised: 17 January 1979
Published: 1 October 1979
James Edgar Keesling
Sibe Mardesic