THE PRODUCT OF SHAPE FIBRATIONS

Abstract

The following fact is shown: Let p : E → B, p : E→ B bemaps of compact Hausdorff spaces. Then p × p : E × E → B × B is a shapefibration if and only if p and p are shape fibrations.Also the following fact onresolutions is shown:Let q = (qλ) : E → E = (Eλ, qλλ, Λ) and r = (rµ) : B → B = (Bµ, rµµ, M )are morphisms of pro-Cpt such that E and B are compact AN R-systems.Then q × r = (qλ× rµ) : E × B → E × B = (Eλ× Bµ, qλλ× rµµ, Λ × M )is a resolution of E × B if and only if q and r are resolutions of E and B,respectively. (Theorem 1)