Abstract
We prove that weak shape equivalences are monomorphisms in the shape category of uniformly pointed movable continua Sh M . We use an example of Draper and Keesling to show that weak shape equivalences need not be monomorphisms in the shape category. We deduce that Sh M is not balanced. We give a characterization of weak dominations in the shape category of pointed continua, in the sense of Dydak (1979). We introduce the class of pointed movable triples ( X, F, Y), for a shape morphism F : X → Y, and we establish an infinite-dimensional Whitehead theorem in shape theory from which we obtain, as a corollary, that for every pointed movable pair of continua ( Y, X) the embedding j : X → Y is a shape equivalence iff it is a weak shape equivalence.
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