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On the shape asphericity of compacta

Yokoi K.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 3

249-264

Dydak and the autor [1] introduced the notion of shape aspherical compacta: a compactum X is shape aspherical if any map f : X --> P from X to a polyhedron P factors up to homotopy as f[...] hog, where g : X --> K, h : K --> P and K is an aspherical CW-complex (i.e., K is a K (G,1)), and modified some results known to be true for the class of strongly hereditarily aspherical compacta, which is introduced by Daverman [2]. In this paper, we shall investigate fundamental properties of the (shape) asphericity.