Vol. 72, No. 1, 1977

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On product of shape and a question of Sher

Y. Kodama

Vol. 72 (1977), No. 1, 115–134

In this paper the products in various shape categories are investigated. In the weak shape category defined by Borsuk, for arbitrary metrizable spaces X and Y there exists always the product ShW(X) × ShW(Y ). In the shape category in the sense of Fox, if X is a pointed FANR and Y is an arbitrary metrizable space, there exists the product ShF(X)× ShF(Y ) and the relation ShF(X) × ShF(Y ) = ShF(X × Y ) holds. In the proper shape category in the sense of Ball and Sher, the product does not exist generally. If X is a compactum and Y is a locally compact metrizable space, the proper shape of the product space X × Y is determined uniquely by the proper shapes of X and Y .

Mathematical Subject Classification
Primary: 55D99, 55D99
Received: 14 July 1976
Revised: 16 February 1977
Published: 1 September 1977
Y. Kodama